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Message boards : Wieferich and Wall-Sun-Sun Prime Search : Ratio between near-WW primes

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Bur
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Message 147654 - Posted: 18 Jan 2021 | 13:56:09 UTC

I was wondering if the probability for near-WW primes is linear with A. It feels like it should be (which doesn't say much) and from the findings so far it could be true: 8 for |A|<=100 and 98 for |A|<=1000.

If it is, we could very well find a |A|=1 since we're at 10 % done.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

JeppeSN

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Message 147655 - Posted: 18 Jan 2021 | 14:29:56 UTC

For a prime, say p = 1212976000000000003 (taken as any prime near the current leading edge), there are 1212976000000000003 different values of A which we would expect (if we do not know anything else) to be equally probable. These are:

-606488000000000001 -606488000000000000 -606487999999999999 -606487999999999998 ... -3 -2 -1 0 +1 +2 +3 ... +606487999999999998 +606487999999999999 +606488000000000000 +606488000000000001
There are 1800 values with 100 < |A| <= 1000.
There are 180 values with 10 < |A| <= 100.
There are 20 values with 0 < |A| <= 10.
There is 1 value with A = 0.

So in the long run, we expect the counts in the "categories" to be in the ratio 1800 : 180 : 20 : 1.

Just one single prime in the A = 0 category will earn eternal fame to PrimeGrid. Statistically, expect about 1 such prime when we have 1800 primes in 100 < |A| <= 1000.

/JeppeSN

Yves Gallot
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Message 147658 - Posted: 18 Jan 2021 | 16:49:57 UTC

The probability for near-primes is linear with A.

The ending point for PrimeGrid's prior Wieferich search on PRPNet is 6.07132e17 and for Wall-Sun-Sun search is 2.6438336e17.

If p = 12e17 (the current leading edge),
the expected number of Wieferich near-primes with |A| <= 1000 is (log(log(12e17)) - log(log(6.07132e17))) * 2001 ~ 33
the expected number of Wall-Sun-Sun near-primes with |A| <= 1000 is (log(log(12e17)) - log(log(2.6438336e17))) * 2001 ~ 74

28 Wieferich and 70 Wall-Sun-Sun near-primes were found with |A| <= 1000.

For |A| <= 10, the expected number of Wieferich and Wall-Sun-Sun near-primes is (33 + 74) / 100 ~ 1.

Bur
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Message 147938 - Posted: 27 Jan 2021 | 15:49:45 UTC - in response to Message 147658.

So far the results match nicely with 13 and 130. I'm not so sure it holds when it comes to A = 0.

We don't look at the actual remainder, but at A = remainder/p, right? So it accomodates for the decreasing prime density at increasing size of the numbers. Thus my feeling is, A = 0 = remainder, will be much less probable and it's probability decreases with increasing size of the number - same as the prime density decreases.

Even more so, if 1800 for |A|<=1000 is really sufficient to produce a Wieferich or WSS prime, then we are 8% there? That seems way too easy to me. If 1.5E18 is 8%, we'd find one within 2E19.

Also I read the density of Wieferich primes is log(log(n)) for 1 to n. Given that 2 are already known, we'd need to go up to 10^1000 to have a good chance to find another one. Even if we chalk one of them up to pure chance, another would be due only within 1...10^100. Far beyond our reach.

Or did I get you wrong?
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

JeppeSN

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Message 147947 - Posted: 27 Jan 2021 | 18:04:48 UTC - in response to Message 147938.

When p (the primes we search) is doubled, the probability in each category (100 < |A| <= 1000, etc.) is halved. So yes, it becomes harder when p grows.

But we think the proportion 1800 : 180 : 20 : 1 should stay the same, as p grows.

The log(log(n)) heuristics is derived from thinking exactly in this way, I would say. Note the following (natural logarithms):
log(log(1.5e+1)) = 1
log(log(1.6e+3)) = 2
log(log(5.3e+9)) = 3
log(log(5.1e+23)) = 4
log(log(2.9e+64)) = 5

So we should find about 1 Wieferich (plus 1 Wall-Sun-Sun) between 5.3e+9 and 5.1e+23. And find the same between 5.1e+23 and 2.9e+64. So this shows how they are supposed to get rarer.

But it should not be "memorizing", so given that the leading edge is near exp(exp(3.7)) right now, no matter how many have been found up to now, we should expect to find about 1 Wieferich (and 1 Wall-Sun-Sun) between now and exp(exp(1 + 3.7)) = 5.6e+47. But you see, we are not able to search that far. So from today and on, we have to be extremely lucky to find anything.

In an old post, I made a graph, I think I can find it.

(Of course, we have no proof these heuristics are correct. In theory, Wieferich primes could be frequent or more rare.)

/JeppeSN

Yves Gallot
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Message 147948 - Posted: 27 Jan 2021 | 18:28:22 UTC - in response to Message 147947.

(Of course, we have no proof these heuristics are correct. In theory, Wieferich primes could be frequent or more rare.)

And WSS primes may not exist if A = 0 is impossible for a currently unknown reason.

JeppeSN

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Message 149200 - Posted: 6 Mar 2021 | 22:49:18 UTC - in response to Message 147655.

Me:

There are 1800 values with 100 < |A| <= 1000.
There are 180 values with 10 < |A| <= 100.
There are 20 values with 0 < |A| <= 10.
There is 1 value with A = 0.

So in the long run, we expect the counts in the "categories" to be in the ratio 1800 : 180 : 20 : 1.

Just one single prime in the A = 0 category will earn eternal fame to PrimeGrid. Statistically, expect about 1 such prime when we have 1800 primes in 100 < |A| <= 1000.

I just realied the stats page does not use:
100 < |A| <= 1000
10 < |A| <= 100
0 < |A| <= 10
A = 0

It uses:
0 <= |A| <= 1000
0 <= |A| <= 100
0 <= |A| <= 10
A = 0

So the ratio with that is simply 2001 : 201 : 21 : 1.

/JeppeSN

Bur
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Message 149782 - Posted: 1 Apr 2021 | 8:47:38 UTC

edit: I only saw Jeppe's post about the stats page now, so I adjusted the number accordingly.

I made a table comparing the actual number of |A| in each category with the expected number, iff (oh yeah) 2001:201:21:1 is correct. I only re-distributed the number of near-WW to follow that ratio, this is by no means a calculation of the expected total number of near-WW.

Number of near-WW found: 201 Distribution: |A|<= | Actual | Expected -------|--------|---------- 1000 | 201 | - 100 | 24 | 20 10 | 1 | 2 0 | 0 | 0 Based on the current number of near-WW found, the probability for a WW or Wieferich prime is: 10 %. At 1.8e19 we would reach: 56 %. 100 % would be reached at: 3.2e19.

The "forecast" was made by taking the current upper bound of tested numbers.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 149868 - Posted: 6 Apr 2021 | 7:38:44 UTC

Update

Tests upper bound: 3.3e18 / 18e18 (18 %) Number of near-WW found: 205 Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 205 | - | - 100 | 24 | 21 | +14 % 10 | 1 | 2 | -50 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 10 %. At 18e18 we would reach: 53 %. 100 % would be reached at: 34e18.

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150028 - Posted: 12 Apr 2021 | 5:49:46 UTC

Update

Tests upper bound: 3.7e18 / 18e18 (21 %) Number of near-WW found: 214 Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 214 | - | - 100 | 25 | 21 | +19 % 10 | 1 | 2 | -50 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 11 %. At 18e18 we would reach: 54 %. 100 % would be reached at: 34e18.

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150139 - Posted: 19 Apr 2021 | 5:54:28 UTC - in response to Message 150028.

Update

Tests upper bound: 4.3e18 / 18e18 (24 %) Number of near-WW found: 224 Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 224 | - | - 100 | 26 | 23 | +13 % 10 | 1 | 2 | -50 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 11 %. At 18e18 we would reach: 46 %. 100 % would be reached at: 39e18.

What the prediction doesn't take into account is that the near-WWs are apparently getting more rare with increasing p.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150194 - Posted: 26 Apr 2021 | 13:35:52 UTC - in response to Message 150139.

Update 26-04-2021

Tests upper bound: 4.6e18 / 18e18 (26 %, +2 %) Number of near-WW found: 234 (+10) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 234 | - | - 100 | 27 | 24 | +13 % 10 | 1 | 2 | -50 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 12 % (+ 1%). At 18e18 we would reach: 47 % (+1 %). 100 % would be reached at: 38e18 (-1e18).

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150285 - Posted: 3 May 2021 | 8:02:15 UTC - in response to Message 150194.

Update 03-05-2021

Tests upper bound: 4.8e18 / 18e18 (27 %, +1 %) Number of near-WW found: 236 (+2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 236 | - | - 100 | 28 | 24 | +17 % 10 | 1 | 2 | -50 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 12 % (+ 0%). At 18e18 we would reach: 44 % (-3 %) 100 % would be reached at: 41e18 (+3e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150354 - Posted: 10 May 2021 | 7:12:10 UTC - in response to Message 150285.

Update 10-05-2021

Tests upper bound: 5.1e18 / 18e18 (28 %, +1 %) Number of near-WW found: 240 (+4) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 240 | - | - 100 | 29 | 24 | +21 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 12 % (+ 0%). At 18e18 we would reach: 42 % (-2 %) 100 % would be reached at: 43e18 (+2e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Ravi Fernando
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Message 150368 - Posted: 10 May 2021 | 20:16:36 UTC - in response to Message 150139.

What the prediction doesn't take into account is that the near-WWs are apparently getting more rare with increasing p.

They are--so much so that the expected number of WW's in a range [a, b] is best modeled not as const * (b-a) but as log log b - log log a. For example, the previously unsearched range of WW is [2.63691e17, 5.14e18] for WSS and [5.97077e17, 5.14e18] for Wieferich, so one would expect about 0.0714 new WSS primes and 0.0513 new Wieferich primes, along with 143 and 103 near-finds (i.e. 2001x more) respectively. We've actually found 141 and 99 respectively, with two more Wieferich near-finds currently waiting for double-checkers. Pretty accurate!

Unfortunately, this means that we've already missed our best shot. The same formula predicts about 58 more near-finds of each of the two types below 2^64, with about 0.0292 actual finds of each type. So overall about a 6% chance of success.

Bur
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Message 150436 - Posted: 17 May 2021 | 7:08:44 UTC - in response to Message 150368.

Thanks Ravi, is it still correct to estimate the expected number of near-WW and WW from the actual number of near-WW found? I.e. what I do with that table.

Update 17-05-2021

Tests upper bound: 5.4e18 / 18e18 (30 %, +3 %) Number of near-WW found: 247 (+7) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 247 | - | - 100 | 30 | 25 | +20 % 10 | 1 | 2 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 12 % (+ 0%). At 18e18 we would reach: 42 % (-0 %) 100 % would be reached at: 43e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Ravi Fernando
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Message 150442 - Posted: 17 May 2021 | 15:59:25 UTC - in response to Message 150436.

Yes, the table looks good to me.

Bur
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Message 150479 - Posted: 25 May 2021 | 6:47:43 UTC - in response to Message 150442.

Update 03-25-2021

Tests upper bound: 5.6e18 / 18e18 (31 %, +1 %) Number of near-WW found: 250 (+3) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 250 | - | - 100 | 30 | 25 | +20 % 10 | 1 | 2 | -50 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 1%). At 18e18 we would reach: 40 % (-2 %) 100 % would be reached at: 45e18 (+2e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150542 - Posted: 1 Jun 2021 | 8:58:46 UTC - in response to Message 150479.

Update 06-01-2021

Tests upper bound: 5.7e18 / 18e18 (32 %, +1 %) Number of near-WW found: 251 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 251 | - | - 100 | 30 | 25 | +20 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 40 % (-0 %) 100 % would be reached at: 46e18 (+e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150571 - Posted: 7 Jun 2021 | 6:30:54 UTC - in response to Message 150542.

Update 06-07-2021

Tests upper bound: 5.9e18 / 18e18 (33 %, +1 %) Number of near-WW found: 255 (+4) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 255 | - | - 100 | 30 | 26 | +15 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 39 % (-1 %) 100 % would be reached at: 46e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150634 - Posted: 14 Jun 2021 | 13:54:53 UTC

Update 06-14-2021

Tests upper bound: 6.0e18 / 18e18 (33 %, +0 %) Number of near-WW found: 256 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 256 | - | - 100 | 30 | 26 | +15 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 38 % (-1 %) 100 % would be reached at: 47e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150685 - Posted: 21 Jun 2021 | 16:46:02 UTC

Update 06-21-2021

Tests upper bound: 6.1e18 / 18e18 (34 %, +1 %) Number of near-WW found: 259 (+3) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 259 | - | - 100 | 30 | 26 | +15 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 38 % (+0 %) 100 % would be reached at: 47e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150715 - Posted: 28 Jun 2021 | 10:06:45 UTC

Update 06-28-2021

Tests upper bound: 6.3e18 / 18e18 (35 %, +1 %) Number of near-WW found: 262 (+3) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 262 | - | - 100 | 30 | 26 | +15 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 37 % (-1 %) 100 % would be reached at: 48e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150761 - Posted: 5 Jul 2021 | 12:32:27 UTC

Update 07-05-2021

Tests upper bound: 6.4e18 / 18e18 (36 %, +1 %) Number of near-WW found: 265 (+3) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 265 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 37 % (-0 %) 100 % would be reached at: 48e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150801 - Posted: 12 Jul 2021 | 9:15:40 UTC - in response to Message 150761.

Update 07-12-2021

Tests upper bound: 6.6e18 / 18e18 (37 %, +1 %) Number of near-WW found: 267 (+2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 267 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 36 % (-0 %) 100 % would be reached at: 50e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150864 - Posted: 19 Jul 2021 | 7:33:38 UTC - in response to Message 150801.

Update 19-07-2021

Tests upper bound: 6.7e18 / 18e18 (37 %, +0 %) Number of near-WW found: 267 (+-0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 267 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+- 0%). At 18e18 we would reach: 36 % (-0 %) 100 % would be reached at: 50e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 150954 - Posted: 26 Jul 2021 | 6:24:53 UTC - in response to Message 150864.

Update 26-07-2021

Tests upper bound: 6.8e18 / 18e18 (38 %, +1 %) Number of near-WW found: 268 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 268 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 36 % (-0 %) 100 % would be reached at: 51e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151006 - Posted: 3 Aug 2021 | 9:24:08 UTC - in response to Message 150954.

Update 03-08-2021

Tests upper bound: 7.0e18 / 18e18 (39 %, +1 %) Number of near-WW found: 269 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 269 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 13 % (+ 0%). At 18e18 we would reach: 35 % (-1 %) 100 % would be reached at: 52e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151063 - Posted: 9 Aug 2021 | 8:57:14 UTC - in response to Message 151006.

Update 09-08-2021

Tests upper bound: 7.1e18 / 18e18 (39 %, +0 %) Number of near-WW found: 270 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 270 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 1%). At 18e18 we would reach: 34 % (-1 %) 100 % would be reached at: 53e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151176 - Posted: 17 Aug 2021 | 6:07:24 UTC - in response to Message 151063.

Update 17-08-2021

Tests upper bound: 7.2e18 / 18e18 (40 %, +1 %) Number of near-WW found: 272 (+2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 272 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 34 % (-0 %) 100 % would be reached at: 53e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151262 - Posted: 24 Aug 2021 | 6:11:25 UTC

Update 24-08-2021

Tests upper bound: 7.4e18 / 18e18 (41 %, +1 %) Number of near-WW found: 273 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 273 | - | - 100 | 30 | 27 | +11 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 33 % (-1 %) 100 % would be reached at: 54e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151330 - Posted: 31 Aug 2021 | 6:01:53 UTC - in response to Message 151262.

Update 31-08-2021

Tests upper bound: 7.6e18 / 18e18 (42 %, +1 %) Number of near-WW found: 274 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 274 | - | - 100 | 30 | 28 | +7 % 10 | 1 | 3 | -67 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 32 % (-1 %) 100 % would be reached at: 56e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151442 - Posted: 9 Sep 2021 | 9:43:05 UTC

A lot of finds this week (ok, 1.5 weeks) and also a WSS with A=-1!

Update 09-09-2021

Tests upper bound: 7.7e18 / 18e18 (43 %, +1 %) Number of near-WW found: 279 (+5) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 279 | - | - 100 | 31 | 28 | +11 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 33 % (+1 %) 100 % would be reached at: 55e18 (-1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151500 - Posted: 13 Sep 2021 | 7:35:58 UTC - in response to Message 151442.

Update 13-09-2021

Tests upper bound: 7.8e18 / 18e18 (43 %, +0 %) Number of near-WW found: 279 (+0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 279 | - | - 100 | 31 | 28 | +11 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 32 % (-1 %) 100 % would be reached at: 56e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151583 - Posted: 20 Sep 2021 | 6:16:20 UTC - in response to Message 151500.

Update 20-09-2021

Tests upper bound: 8.0e18 / 18e18 (44 %, +1 %) Number of near-WW found: 281 (+2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 281 | - | - 100 | 31 | 28 | +11 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 32 % (-0 %) 100 % would be reached at: 57e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151643 - Posted: 27 Sep 2021 | 12:27:30 UTC

Update 27-09-2021

Tests upper bound: 8.1e18 / 18e18 (45 %, +1 %) Number of near-WW found: 283 (+2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 283 | - | - 100 | 31 | 28 | +11 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 31 % (-1 %) 100 % would be reached at: 57e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151688 - Posted: 4 Oct 2021 | 12:07:21 UTC - in response to Message 151643.

Update 04-10-2021

Tests upper bound: 8.3e18 / 18e18 (46 %, +1 %) Number of near-WW found: 283 (+-0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 283 | - | - 100 | 31 | 28 | +11 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+- 0%). At 18e18 we would reach: 31 % (-1 %) 100 % would be reached at: 59e18 (+2e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Nick

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Message 151690 - Posted: 4 Oct 2021 | 13:27:51 UTC

I could understand this if you said - percentage wise - how much worse the chances are getting.
Compared to first estimate.
Compared to recent.

Bur
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Message 151739 - Posted: 11 Oct 2021 | 6:23:59 UTC - in response to Message 151690.

You can see that from the ever decreasing "At 18e18 we would reach:" value. It decreases because we find fewer and fewer near hits. Or did you mean something else?

Honestly, I'm not really convinced it makes sense as a forecast (likely it doesn't) since it doesn't take into account that these misses already happened and probability doesn't care what did occur. Just because we found no WWS prime with that many nears doesn't mean we're bound to find one with a specific probability.

Anyway, I think it's a nice statistic that shows how the subproject progresses and it also shows that the "nearness" appears to be statistically distributed as JeppeSN suggested.

Update 11-10-2021

Tests upper bound: 8.5e18 / 18e18 (47 %, +1 %) Number of near-WW found: 285 (+2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 285 | - | - 100 | 31 | 28 | +7 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 30 % (-1 %) 100 % would be reached at: 60e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 151835 - Posted: 18 Oct 2021 | 6:26:38 UTC - in response to Message 151739.

Update 18-10-2021

Tests upper bound: 8.7e18 / 18e18 (48 %, +1 %) Number of near-WW found: 288 (+3) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 288 | - | - 100 | 31 | 28 | +7 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 14 % (+ 0%). At 18e18 we would reach: 30 % (-0 %) 100 % would be reached at: 60e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 152117 - Posted: 5 Nov 2021 | 11:49:35 UTC

We reached 2^63 of 2^64 tests. At first glance it looks like we're nearly done, but exponentials being counter-intuitive to many people (like me) and it's just half way done... ;)

Update 05-11-2021

Tests upper bound: 9.2234e18 / 18e18 = 2^63 / 2^64 (50 %, +1 %) Number of near-WW found: 299 (+4) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 299 | - | - 100 | 31 | 30 | +3 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (+ 1%). At 18e18 we would reach: 29 % (-1 %) 100 % would be reached at: 62e18 (+2e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 152180 - Posted: 9 Nov 2021 | 14:48:44 UTC - in response to Message 152117.

Update 09-11-2021

Tests upper bound: 9.3e18 / 18e18 (51 %, +1 %) Number of near-WW found: 301 (+2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 301 | - | - 100 | 33 | 30 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (+ 1%). At 18e18 we would reach: 29 % (-0 %) 100 % would be reached at: 62e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 152269 - Posted: 15 Nov 2021 | 9:29:30 UTC - in response to Message 152180.

Update 15-11-2021

Tests upper bound: 9.4e18 / 18e18 (51 %, +0 %) Number of near-WW found: 302 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 302 | - | - 100 | 33 | 30 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (+ 1%). At 18e18 we would reach: 29 % (-0 %) 100 % would be reached at: 62e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 152347 - Posted: 22 Nov 2021 | 8:06:25 UTC - in response to Message 152269.

Update 22-11-2021

Tests upper bound: 9.5e18 / 18e18 (52 %, +1 %) Number of near-WW found: 302 (+-0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 302 | - | - 100 | 33 | 30 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (- 0%). At 18e18 we would reach: 29 % (-0 %) 100 % would be reached at: 63e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 152442 - Posted: 2 Dec 2021 | 6:39:02 UTC

A bit late...

Update 29-11-2021

Tests upper bound: 9.6e18 / 18e18 (52 %, +0 %) Number of near-WW found: 305 (+3) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 305 | - | - 100 | 34 | 31 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (- 0%). At 18e18 we would reach: 29 % (-0 %) 100 % would be reached at: 63e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 152634 - Posted: 13 Dec 2021 | 14:47:43 UTC - in response to Message 152442.

Things were slow. The GFN-challenge seems to have drained GPU power from WWSS. My 1660 Super will be back soon though, so expect a big speed-up next week.

Update 13-12-2021

Tests upper bound: 9.8e18 / 18e18 (53 %, +0 %) Number of near-WW found: 308 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 308 | - | - 100 | 34 | 31 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (+ 0%). At 18e18 we would reach: 29 % (-0 %) 100 % would be reached at: 64e18 (+1e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 152747 - Posted: 20 Dec 2021 | 10:52:31 UTC - in response to Message 152634.

No new near-WWSSprimes this week. Not unexpected, since during the challenge the completion rate had dropped from 14k/day to 5k/day. It's back up again though, so unless many computers take a break over the christmas holidays, hopefully this week will fare better again.

Update 20-12-2021

Tests upper bound: 9.9e18 / 18e18 (54 %, +1 %) Number of near-WW found: 308 (+-0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 308 | - | - 100 | 34 | 31 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 15 % (+- 0%). At 18e18 we would reach: 29 % (-0 %) 100 % would be reached at: 64e18 (+0e18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 153038 - Posted: 3 Jan 2022 | 14:34:21 UTC - in response to Message 152747.

Update 03-01-2022

Last update ist two weeks back, so mind that when looking at the differences. And we reached 1e19. Only 8 quintillion numbers left!

Tests upper bound: 10.1E18 / 18E18 (55 %, +1 %) Number of near-WW found: 310 (+-2) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 310 | - | - 100 | 34 | 31 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 16 % (+ 1%). At 18e18 we would reach: 28 % (-1 %) 100 % would be reached at: 65E18 (+1E18)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

JeppeSN

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Message 153042 - Posted: 3 Jan 2022 | 17:58:09 UTC - in response to Message 153038.

Cool. The rest of the discoveries we do, will have twenty digits, like 10017779178182939981 by Grzegorz Roman Granowski. /JeppeSN

Bur
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Message 153161 - Posted: 10 Jan 2022 | 11:03:35 UTC

Update 10-01-2022

Tests upper bound: 10.2e18 / 18e18 (55 %, +0 %) Number of near-WW found: 311 (+-1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 311 | - | - 100 | 34 | 31 | +10 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 16 % (+ 1%). At 18e18 we would reach: 28 % (-0 %) 100 % would be reached at: 66e18 (+1e18) Last week average numbers tested per day: 1.41E16 (+- N/A) ETA project completion: 582 days (+- N/A)

Things are still slow, last week's average is 9400 completed tasks/day. Due to DC that corresponds to 14E16 numbers checked / day. At that rate it'll be 582 days to complete the project. I added that to the stats.
____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Dave

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Message 153164 - Posted: 10 Jan 2022 | 12:28:05 UTC

582 days could be a best case therefore but if loads of people jump on it how dramatically could that come down? I'm playing safe & only parking at 1.1B credit - 2B would take me nearly all year but only assuming enough work!

Yves Gallot
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Message 153176 - Posted: 10 Jan 2022 | 16:56:57 UTC - in response to Message 153164.

582 days could be a best case therefore but if loads of people jump on it how dramatically could that come down? I'm playing safe & only parking at 1.1B credit - 2B would take me nearly all year but only assuming enough work!

WW has been running for 380 days and the leading edge is 10,200 P.
Then the remaining time is 380 * (2^64/10200e15) - 380 = 307 days.
The Riemann's Birthday Challenge (17-20 September) could be the end of the project.

JeppeSN

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Message 153179 - Posted: 10 Jan 2022 | 21:02:19 UTC - in response to Message 153176.

The Riemann's Birthday Challenge (17-20 September) could be the end of the project.

It would be an unusual challenge if we ran out of work before the end of the challenge. /JeppeSN

Bur
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Message 153318 - Posted: 17 Jan 2022 | 11:15:55 UTC - in response to Message 153179.

Yes, it's only the ETA based on last week's numbers. I clarified that in the stats.

Update 17-01-2022

Tests upper bound: 10.3e18 / 18e18 (56 %, +1 %) Number of near-WW found: 312 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 312 | - | - 100 | 35 | 31 | +13 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 16 % (+ 0%). At 18e18 we would reach: 28 % (-0 %) 100 % would be reached at: 66e18 (+0e18) Last week average numbers tested per day: 13.3E15 (-0.8E15) ETA project completion (based on last week only): 609 days (+ 27 days)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 153530 - Posted: 24 Jan 2022 | 7:27:41 UTC - in response to Message 153318.

Update 24-01-2022

Tests upper bound: 10.4e18 / 18e18 (57 %, +1 %) Number of near-WW found: 313 (+1) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 313 | - | - 100 | 35 | 31 | +13 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 16 % (+ 0%). At 18e18 we would reach: 28 % (-0 %) 100 % would be reached at: 67e18 (+1e18) Last week average numbers tested per day: 12.2E15 (-1.1E15) ETA project completion (based on last week only): 657 days (+ 46 days)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 153731 - Posted: 1 Feb 2022 | 6:51:04 UTC

No new near-hit. High GPU prices are hurting innocent DC-project! The humanity!

Update 01-01-2022

Tests upper bound: 10.5e18 / 18e18 (57 %, +0 %) Number of near-WW found: 313 (+-0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 313 | - | - 100 | 35 | 31 | +13 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 16 % (+-0%). At 18e18 we would reach: 27 % (-1 %) 100 % would be reached at: 67e18 (+1e18) Last week average numbers tested per day: 16.0E15 (+3.8E15) ETA project completion (based on last week only): 494 days (- 163 days)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Bur
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Message 153998 - Posted: 7 Feb 2022 | 8:19:34 UTC

Update 07-02-2022

Tests upper bound: 10.5e18 / 18e18 (57 %, +0 %) Number of near-WW found: 313 (+-0) Distribution: |A|<= | Actual | Expected | Deviation -------|--------|----------|----------- 1000 | 313 | - | - 100 | 35 | 31 | +13 % 10 | 2 | 3 | -33 % 0 | 0 | 0 | 0 % Based on the current number of near-WW found, the probability for a WW prime is: 16 % (+-0%). At 18e18 we would reach: 27 % (-0 %) 100 % would be reached at: 67e18 (+0e18) Last week average numbers tested per day: 8.6E15 (-7.4E15) ETA project completion (based on last week only): 922 days (+ 428 days)

____________
1281979 * 2^485014 + 1 is prime ... no further hits up to: n = 5,700,000

Dr Who Fan

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Message 154875 - Posted: 18 Mar 2022 | 20:54:26 UTC

Just curious if Bur might of forgotten to update this sub project stats. Hopefully everything is OK for him.

Grzegorz Roman Granowski

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Message 155145 - Posted: 16 Apr 2022 | 14:03:20 UTC

Greetings ... will there be an update ... regarding WW ?

the last was over 2 months ago !

regards, Grzegorz Roman Granowski
____________

dannyridel
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Message 155203 - Posted: 24 Apr 2022 | 21:33:59 UTC

I think he might just have gotten tired of this or forgot-he was last online 10 days ago on mersenneforum.
____________
My lucky number is 6219*2^3374198+1

Michael Millerick
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Message 155221 - Posted: 25 Apr 2022 | 20:34:36 UTC

The leading edge is 11,706.982 P (visible on http://www.primegrid.com/server_status_subprojects.php), which means that the project is just over 65% now.
____________

Nick

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Message 155768 - Posted: 4 Jun 2022 | 14:45:20 UTC - in response to Message 155221.

The leading edge is 11,706.982 P (visible on http://www.primegrid.com/server_status_subprojects.php), which means that the project is just over 65% now.

I am confused if this tells us how much the project is finished on an on-going basis.
How, please, can I work out how much is left to be done?
The rate this has picked up recently, WW may not be a viable challenge in September.

Michael Millerick
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Message 155770 - Posted: 4 Jun 2022 | 15:17:44 UTC - in response to Message 155768.

The leading edge is 11,706.982 P (visible on http://www.primegrid.com/server_status_subprojects.php), which means that the project is just over 65% now.

I am confused if this tells us how much the project is finished on an on-going basis.
How, please, can I work out how much is left to be done?
The rate this has picked up recently, WW may not be a viable challenge in September.

The leading edge is now 12,612.271P. The limit of the software for project is 18,000P, so that is when the project will end. So we are at 70% now.

For reference, each work unit advances the project by .003P, so my 3070 is advancing the project by about .270P each day.
____________

Nick

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Message 155775 - Posted: 4 Jun 2022 | 17:10:21 UTC - in response to Message 155770.

The leading edge is 11,706.982 P (visible on http://www.primegrid.com/server_status_subprojects.php), which means that the project is just over 65% now.

I am confused if this tells us how much the project is finished on an on-going basis.
How, please, can I work out how much is left to be done?
The rate this has picked up recently, WW may not be a viable challenge in September.

The leading edge is now 12,612.271P. The limit of the software for project is 18,000P, so that is when the project will end. So we are at 70% now.

For reference, each work unit advances the project by .003P, so my 3070 is advancing the project by about .270P each day.

I like to use the force in these calculations - oh crap - I won't get the next badge.
But I am going to go for it.
It is worthwhile - to try.

Michael Millerick
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Message 155778 - Posted: 4 Jun 2022 | 18:25:52 UTC - in response to Message 155775.

The leading edge is 11,706.982 P (visible on http://www.primegrid.com/server_status_subprojects.php), which means that the project is just over 65% now.

I am confused if this tells us how much the project is finished on an on-going basis.
How, please, can I work out how much is left to be done?
The rate this has picked up recently, WW may not be a viable challenge in September.

The leading edge is now 12,612.271P. The limit of the software for project is 18,000P, so that is when the project will end. So we are at 70% now.

For reference, each work unit advances the project by .003P, so my 3070 is advancing the project by about .270P each day.

I like to use the force in these calculations - oh crap - I won't get the next badge.
But I am going to go for it.
It is worthwhile - to try.

Ironically the more of us that go for badges, the less likely any of us are to be able to progress. My plan is to stick it out here on WW at least until I get to 200m credit in a couple months or until the project runs dry. Weâ€™ll see which comes first and how I feel at that point.
____________

Nick

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Message 155784 - Posted: 4 Jun 2022 | 20:21:19 UTC - in response to Message 155778.

The leading edge is 11,706.982 P (visible on http://www.primegrid.com/server_status_subprojects.php), which means that the project is just over 65% now.

I am confused if this tells us how much the project is finished on an on-going basis.
How, please, can I work out how much is left to be done?
The rate this has picked up recently, WW may not be a viable challenge in September.

The leading edge is now 12,612.271P. The limit of the software for project is 18,000P, so that is when the project will end. So we are at 70% now.

For reference, each work unit advances the project by .003P, so my 3070 is advancing the project by about .270P each day.

I like to use the force in these calculations - oh crap - I won't get the next badge.
But I am going to go for it.
It is worthwhile - to try.

Ironically the more of us that go for badges, the less likely any of us are to be able to progress. My plan is to stick it out here on WW at least until I get to 200m credit in a couple months or until the project runs dry. Weâ€™ll see which comes first and how I feel at that point.

That is the pragmatic approach.
Unfortunately (and this is great for getting the work done) there are lunatics that want to crunch more than other crunchers.
I put my hand up. I am a lunatic. At least in this.
I have noticed people increasing in WW.

JeppeSN

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Message 155798 - Posted: 5 Jun 2022 | 14:27:51 UTC - in response to Message 155770.

The leading edge is now 12,612.271P. The limit of the software for project is 18,000P, so that is when the project will end. So we are at 70% now.

For those who want to be very precise, the limit of the software is:

2^64 = 18'446'744'073'709'551'616

Seems like the current 0.003 P work unit size will take us to 18'446.743 P. Then there will be a fraction of a work unit from there to the software limit.

/JeppeSN

Michael Millerick
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Message 156260 - Posted: 9 Jul 2022 | 19:15:55 UTC

The leading edge is currently 13,385.296P. This means the project is 72.56%. In the last month, the project has averaged 14590 tasks per day, which means the project has about 231 more days before it will be completed at the current rate. There is about 40.49 billion credit left to be claimed for the project.
____________

Michael Millerick
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Message 156363 - Posted: 17 Jul 2022 | 19:51:54 UTC

The leading edge is currently 13,609.720P. This means the project is 73.78% complete. In the last month, the project has averaged 15660 tasks per day, which means the project has about 205 more days before it will be completed at the current rate. There is about 38.69 billion credit left to be claimed for the project.
____________

Michael Millerick
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Message 156480 - Posted: 24 Jul 2022 | 22:49:40 UTC

The leading edge is currently 13,799.158P. This means the project is 74.81% complete. In the last month, the project has averaged 16560 tasks per day, which means the project has about 187 more days before it will be completed at the current rate. There is about 37.18 billion credit left to be claimed for the project.
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GDB

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Message 156536 - Posted: 26 Jul 2022 | 12:59:27 UTC

So, the "âˆž" in the B column for WW on the home page, isn't really true?
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Michael Millerick
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Message 156538 - Posted: 26 Jul 2022 | 13:39:54 UTC - in response to Message 156536.

So, the "âˆž" in the B column for WW on the home page, isn't really true?

It is true from the perspective that the admins do not need to load work for the project and from the perspective that the project could go on forever if the software supported it. Unfortunately the software would need to be rewritten to proceed past a point that we are steadily approaching.
____________

JeppeSN

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Message 156544 - Posted: 26 Jul 2022 | 19:08:12 UTC - in response to Message 156538.

It is true from the perspective that the admins do not need to load work for the project and from the perspective that the project could go on forever if the software supported it. Unfortunately the software would need to be rewritten to proceed past a point that we are steadily approaching.

Also, right now we are checking all primes between 2^63 and 2^64, i.e. all 64-bit primes, to see if any has the Wieferich property or the Wall-Sun-Sun property. If we were to check 65-bit primes (i.e. all the primes up to 2^65), then it would be slower because these numbers do not seem to fit as well into the hardware. But as you say, we do not even have appropriate software for it.
There are 425656284035217743 primes with at most 64 bits There are 412246861431389469 primes with exactly 65 bits

So a hypothetical project to go from where WW ends to the next power of two would test almost as many prime numbers as we did in total up to the current software limit. However, the expected chance to find something is smaller for bigger primes, so it would still be very lucky if we found a true Wieferich or Wall-Sun-Sun prime (A=0) in such an interval.

/JeppeSN

Yves Gallot
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Message 156546 - Posted: 26 Jul 2022 | 21:45:07 UTC

For Wall-Sun-Sun prime, it is time to hand over the problem to mathematicians.
No prime for p < 264... probably an hidden property that could be found: no Wall-Sun-Sun prime exists.

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Message 156550 - Posted: 27 Jul 2022 | 9:21:10 UTC

I think Wall-Sun-Sun primes exist. /JeppeSN

Michael Millerick
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Message 156631 - Posted: 31 Jul 2022 | 20:41:05 UTC

The leading edge is currently 13,966.825P. This means the project is 75.71% complete. In the last month, the project has averaged 16790 tasks per day, which means the project has about 178 more days before it will be completed at the current rate. There is about 35.84 billion credit left to be claimed for the project.
____________

Michael Millerick
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Message 156691 - Posted: 7 Aug 2022 | 15:03:53 UTC

The leading edge is currently 14,149.069P. This means the project is 76.70% complete. In the last month, the project has averaged 17160 tasks per day, which means the project has about 167 more days before it will be completed at the current rate. There is about 34.38 billion credit left to be claimed for the project.
____________

JeppeSN

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Message 156692 - Posted: 7 Aug 2022 | 18:00:58 UTC - in response to Message 156691.

means the project has about 167 more days before it will be completed at the current rate.

But there is a WW challenge in 41 days. That will change something. If we do 20 times the normal rate during those 3 days, there could be about two months left after the challenge.

The project could end before the turn of the year.

/JeppeSN

Michael Millerick
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Message 156693 - Posted: 7 Aug 2022 | 18:22:43 UTC - in response to Message 156692.

means the project has about 167 more days before it will be completed at the current rate.

But there is a WW challenge in 41 days. That will change something. If we do 20 times the normal rate during those 3 days, there could be about two months left after the challenge.

The project could end before the turn of the year.

/JeppeSN

It is going to throw off the calculation based on average tasks completed per day as well. It will be an overall strong push towards the end of the project.
____________

Michael Millerick
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Message 156726 - Posted: 14 Aug 2022 | 14:13:38 UTC

The leading edge is currently 14,329.645P. This means the project is 77.68% complete. In the last month, the project has averaged 17640 tasks per day, which means the project has about 156 more days before it will be completed at the current rate. There is about 32.93 billion credit left to be claimed for the project.

The project has been advancing forward by about 1% per week, which means that two different mechanisms for estimating when the project will finish are pretty close to each other. Looks like it will be 5-6 months, ignoring the potentially substantial impact that the challenge will have. If the challenge increases the amount of work done by 20x, then that means that there is really about three months of time left before the project finishes.
____________

Michael Millerick
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Message 156768 - Posted: 21 Aug 2022 | 14:50:55 UTC

The leading edge is currently 14,516.467P. This means the project is 78.69% complete. In the last month, the project has averaged 17330 tasks per day, which means the project has about 151 more days before it will be completed at the current rate. There is about 31.44 billion credit left to be claimed for the project.
____________

Michael Millerick
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Message 156849 - Posted: 28 Aug 2022 | 20:00:21 UTC

The leading edge is currently 14,706.865P. This means the project is 79.73% complete. In the last month, the project has averaged 17430 tasks per day, which means the project has about 143 more days before it will be completed at the current rate. There is about 29.92 billion credit left to be claimed for the project.
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Eudy Silva

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Message 156855 - Posted: 29 Aug 2022 | 10:11:05 UTC - in response to Message 156849.

... This means the project is 79.73% complete. In the last month, the project has averaged 17430 tasks per day, which means the project has about 143 more days before it will be completed at the current rate. ...

The next challenge will be a 3 day WW crunch challenge - September 17-20)
I imagine the boost it will provide.
____________

"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment.

Michael Millerick
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Message 156926 - Posted: 4 Sep 2022 | 14:53:00 UTC

The leading edge is currently 14909.302P.
This means the project is 80.82% complete.
In the last month, the project has averaged 17960 tasks per day, which means the project has about 131 more days before it will be completed at the current monthly rate.
In the last day, the project completed 22050 tasks, which means the project has about 107 more days before it will be completed at the current rate.
There is about 28.3 billion credit left to be claimed for the project.

____________

Grzegorz Roman Granowski

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Message 156943 - Posted: 10 Sep 2022 | 11:30:16 UTC - in response to Message 156926.

Greetings ...

a race should propably speed up the moment of finding A = 0

so let's comptete ...

and regards, Grzegorz Roman Granowski ...
____________

Michael Millerick
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Message 156956 - Posted: 11 Sep 2022 | 19:54:31 UTC

The leading edge is currently 15115.198P.
This means the project is 81.94% complete.
In the last month, the project has averaged 18220 tasks per day, which means the project has about 122 more days before it will be completed at the current monthly rate.
In the last day, the project completed 19050 tasks, which means the project has about 117 more days before it will be completed at the current rate.
There is about 26.65 billion credit left to be claimed for the project.

The next update will be in the middle of the challenge. It will be interesting to see how far the project is catapulted forward by the challenge. My guestimate is that there will be about 60 days of work left after the challenge is over, meaning that we will end at around 92% of the project completed.
____________

Michael Millerick
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Message 157035 - Posted: 18 Sep 2022 | 15:18:45 UTC

The leading edge is currently 15478.615P.
This means the project is 83.91% complete.
In the last month, the project has averaged 20060 tasks per day, which means the project has about 99 more days before it will be completed at the current monthly rate.
In the last day, the project completed 97850 tasks, which means the project has about 20 more days before it will be completed at the current rate. However this is a rate from the challenge, and so it is not representative of when the project will actually finish.
There is about 23.75 billion credit left to be claimed for the project.

____________

Michael Millerick
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Message 157190 - Posted: 26 Sep 2022 | 9:35:03 UTC

The leading edge is currently 16168.447P.
This means the project is 87.65% complete.
In the last month, the project has averaged 31510 tasks per day, which means the project has about 48 more days before it will be completed at the current monthly rate.
In the last day, the project completed 20990 tasks, which means the project has about 72 more days before it will be completed at the current rate.
There is about 18.23 billion credit left to be claimed for the project.

The challenge caused quite the advancement, but there is still likely to be a little more than two months before the project finishes.
____________

Dave

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Message 157201 - Posted: 27 Sep 2022 | 13:03:05 UTC

Parked at 1,100,000,000. I am done.

Michael Millerick
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Message 157276 - Posted: 2 Oct 2022 | 17:04:48 UTC

The leading edge is currently 16319.773P.
This means the project is 88.47% complete.
In the last month, the project has averaged 31410 tasks per day, which means the project has about 45 more days before it will be completed at the current monthly rate.
In the last day, the project completed 15030 tasks, which means the project has about 94 more days before it will be completed at the current rate.
There is about 17.02 billion credit left to be claimed for the project.

____________

Michael Millerick
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Message 157336 - Posted: 9 Oct 2022 | 14:42:25 UTC

The leading edge is currently 16460.521P.
This means the project is 89.23% complete.
In the last month, the project has averaged 30140 tasks per day, which means the project has about 44 more days before it will be completed at the current monthly rate. The monthly completion rate is still very much skewed by the last challenge.
In the last day, the project completed 14640 tasks, which means the project has about 90 more days before it will be completed at the current rate.
There is about 15.89 billion credit left to be claimed for the project.

____________

Michael Millerick
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Message 157438 - Posted: 16 Oct 2022 | 20:12:10 UTC

The leading edge is currently 16619.257P.
This means the project is 90.09% complete.
In the last month, the project has averaged 29200 tasks per day, which means the project has about 42 more days before it will be completed at the current monthly rate.
In the last day, the project completed 15500 tasks, which means the project has about 79 more days before it will be completed at the current rate.
There is about 14.62 billion credit left to be claimed for the project.

____________

MiauiKatze

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Message 157452 - Posted: 17 Oct 2022 | 10:55:37 UTC - in response to Message 157438.

The leading edge is currently 16619.257P. ...
...about 42 more days before it will be completed at the current monthly rate.

So this is the last chance for badges?

____________
--------
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Dave

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Message 157458 - Posted: 17 Oct 2022 | 15:05:43 UTC - in response to Message 157452.

Yep.

Michael Millerick
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Message 157460 - Posted: 17 Oct 2022 | 15:46:08 UTC - in response to Message 157452.

The leading edge is currently 16619.257P. ...
...about 42 more days before it will be completed at the current monthly rate.

So this is the last chance for badges?

It's actually going to be closer to the 79 day estimate since the monthly rate is still skewed by the challenge that happened a couple weeks ago, although these estimates will be more volatile as the amount of remaining work decreases and people either pile onto the project to burn towards their goals at the end, or they drop off of the project once they have reached their goals.
____________

Nick

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Message 157462 - Posted: 18 Oct 2022 | 1:42:45 UTC - in response to Message 157460.

The leading edge is currently 16619.257P. ...
...about 42 more days before it will be completed at the current monthly rate.

So this is the last chance for badges?

It's actually going to be closer to the 79 day estimate since the monthly rate is still skewed by the challenge that happened a couple weeks ago, although these estimates will be more volatile as the amount of remaining work decreases and people either pile onto the project to burn towards their goals at the end, or they drop off of the project once they have reached their goals.

Or random things happen, like me starting up WW again.
I think the polite thing to do is to not do WW.
Which is ultimately bemusing.
Maybe it is good practice to consider things that don't matter?
I am not saying maths doesn't matter - it is the only subject that can be true?
(It came to light a little difficulty with the axioms, which I understand that Mathematicians have correctly ignored. Not even Maths is able to be fully abstracted from the uncertainty of reality)

I am not sure who set off this frenzy at the pointy end of the project - I apologise if it was me.

Edit: I am hugely exaggerating about the frenzy part - I have seen only one other person start up again.

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Message 157466 - Posted: 18 Oct 2022 | 18:39:06 UTC - in response to Message 157462.

I think the polite thing to do is to not do WW.

No. /JeppeSN

Monkeydee
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Message 157467 - Posted: 19 Oct 2022 | 2:13:38 UTC - in response to Message 157466.

I think the polite thing to do is to not do WW.

No. /JeppeSN

More to the point if everyone stops so "someone else" can reach their goals then the project may never finish
Someone has to be a little greedy to finish things up
____________
My Primes
Badge Score: 4*2 + 6*2 + 7*6 + 8*6 + 11*3 + 12*1 = 155

Michael Millerick
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Message 157537 - Posted: 23 Oct 2022 | 18:40:50 UTC

The leading edge is currently 16800.127P.
This means the project is 91.07% complete.
In the last month, the project has averaged 21640 tasks per day, which means the project has about 51 more days before it will be completed at the current monthly rate. This rate is still somewhat elevated because it takes into account part of the last challenge on WW.
In the last day, the project completed 18010 tasks, which means the project has about 61 more days before it will be completed at the current rate.
There is about 13.17 billion credit left to be claimed for the project.

____________

Michael Millerick
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Message 157600 - Posted: 30 Oct 2022 | 20:14:20 UTC

The leading edge is currently 17002.099P.
This means the project is 92.17% complete.
In the last month, the project has averaged 16130 tasks per day, which means the project has about 60 more days before it will be completed at the current monthly rate.
In the last day, the project completed 18920 tasks, which means the project has about 51 more days before it will be completed at the current rate.
There is about 11.56 billion credit left to be claimed for the project.

These estimates are no longer biased by the challenge.
____________

Michael Millerick
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Message 157709 - Posted: 6 Nov 2022 | 15:22:10 UTC

The leading edge is currently 17191.03P.
This means the project is 93.19% complete.
In the last month, the project has averaged 16800 tasks per day, which means the project has about 50 more days before it will be completed at the current monthly rate.
In the last day, the project completed 18090 tasks, which means the project has about 46 more days before it will be completed at the current rate.
There is about 10.05 billion credit left to be claimed for the project.

____________

Michael Millerick
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Message 157812 - Posted: 13 Nov 2022 | 20:40:09 UTC

The leading edge is currently 17393.377P.
This means the project is 94.29% complete.
In the last month, the project has averaged 17770 tasks per day, which means the project has about 40 more days before it will be completed at the current monthly rate.
In the last day, the project completed 18320 tasks, which means the project has about 38 more days before it will be completed at the current rate.
There is about 8.43 billion credit left to be claimed for the project.

____________

Michael Millerick
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Message 157966 - Posted: 20 Nov 2022 | 16:22:14 UTC