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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
Last modified: 18 Jan 2021 | 16:52:39 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.
Last modified: 27 Jan 2021 | 15:51:32 UTC

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.

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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
Last modified: 1 Apr 2021 | 9:28:58 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
Last modified: 6 Apr 2021 | 7:52:14 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.
Last modified: 26 Apr 2021 | 13:40:17 UTC

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.
Last modified: 10 May 2021 | 20:22:18 UTC

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.
Last modified: 7 Jun 2021 | 6:31:28 UTC

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
Last modified: 5 Jul 2021 | 12:33:18 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.
Last modified: 11 Oct 2021 | 6:25:57 UTC

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
Last modified: 10 Jan 2022 | 11:04:48 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.
(Really I am worried about not getting the next badge)

Michael Millerick
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Message 155770 - Posted: 4 Jun 2022 | 15:17:44 UTC - in response to Message 155768.
Last modified: 4 Jun 2022 | 15:20:53 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.

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.
(Really I am worried about not getting the next badge)

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.
(Really I am worried about not getting the next badge)

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.
(Really I am worried about not getting the next badge)

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. We’ll see which comes first and how I feel at that point.
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Nick

Joined: 11 Jul 11
Posts: 1955
ID: 105020
Credit: 5,607,480,649
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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.
(Really I am worried about not getting the next badge)

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. We’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

Joined: 5 Apr 14
Posts: 1724
ID: 306875
Credit: 41,343,356
RAC: 13,794

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

so about 18'446.744 P.

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
Volunteer tester

Joined: 4 Feb 09
Posts: 853
ID: 35074
Credit: 578,122,022
RAC: 1,597,902

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
Volunteer tester

Joined: 4 Feb 09
Posts: 853
ID: 35074
Credit: 578,122,022
RAC: 1,597,902

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
Volunteer tester

Joined: 4 Feb 09
Posts: 853
ID: 35074
Credit: 578,122,022
RAC: 1,597,902

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

Joined: 15 Nov 11
Posts: 280
ID: 119185
Credit: 3,383,664,451
RAC: 3,840,659

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

So, the "∞" in the B column for WW on the home page, isn't really true?
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Michael Millerick
Volunteer tester

Joined: 4 Feb 09
Posts: 853
ID: 35074
Credit: 578,122,022
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Message 156538 - Posted: 26 Jul 2022 | 13:39:54 UTC - in response to Message 156536.

So, the "∞" 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

Joined: 5 Apr 14
Posts: 1724
ID: 306875
Credit: 41,343,356
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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
Volunteer developer
Project scientist

Joined: 19 Aug 12
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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.

JeppeSN

Joined: 5 Apr 14
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Credit: 41,343,356
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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
Volunteer tester

Joined: 4 Feb 09
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ID: 35074
Credit: 578,122,022
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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

Joined: 5 Apr 14
Posts: 1724
ID: 306875
Credit: 41,343,356
RAC: 13,794

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
Volunteer tester

Joined: 4 Feb 09
Posts: 853
ID: 35074
Credit: 578,122,022
RAC: 1,597,902

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