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Message boards : News : World Record Primorial Prime

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JohnProject donor
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Message 29946 - Posted: 24 Dec 2010 | 15:29:51 UTC
Last modified: 24 Dec 2010 | 15:31:02 UTC

On 20 Dec 2010, 08:05:22 UTC, PrimeGrid’s PRPNet found the largest known Primorial prime: 843301#-1

The prime is 365,851 digits long and enters Chris Caldwell's The Largest Known Primes Database ranked 1st for Primorial primes and 260th overall.

The discovery was made by Michał Gasewicz of Poland using an Intel dual Xeon E5520 @ 2.27GHz with 12GB RAM, running 64 bit Linux. This computer took about 71 hours and 20 minutes to complete the primality test using pfgw x64. Michał is a member of the BOINC@Poland team.

For more details, please see the official announcement.
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Message 29955 - Posted: 24 Dec 2010 | 19:37:36 UTC

Just curious...why did this prime take so long to test (and to verify)? According to the official announcement, both took ~70 hours apiece, but about a week ago one of my PRPnet clients (on a Core 2 Duo E4500, very similar to the discoverer's computer) fell back to the primorial server and tested 844309#-1 in ~4.5 hours. Considering that the n-value of my test was actually a little bigger than the prime's, surely mine should have taken longer (though they're close enough that I'd expect the difference to be minimal).

The only possible difference I can see is that my computer used 32-bit PFGW, whereas the discoverer's used 64-bit PFGW. Perhaps this is the cause of the discrepancy (though normally 64-bit should be faster)?

JohnProject donor
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321 LLR Bronze: Earned 10,000 credits (11,773)Cullen LLR Bronze: Earned 10,000 credits (14,945)ESP LLR Bronze: Earned 10,000 credits (26,855)PPS LLR Bronze: Earned 10,000 credits (84,876)PSP LLR Bronze: Earned 10,000 credits (15,311)SoB LLR Bronze: Earned 10,000 credits (21,440)SR5 LLR Bronze: Earned 10,000 credits (29,270)SGS LLR Bronze: Earned 10,000 credits (26,616)TPS LLR (retired) Bronze: Earned 10,000 credits (36,288)TRP LLR Bronze: Earned 10,000 credits (41,655)Woodall LLR Bronze: Earned 10,000 credits (15,807)321 Sieve (suspended) Bronze: Earned 10,000 credits (20,014)Cullen/Woodall Sieve (suspended) Bronze: Earned 10,000 credits (23,405)PPS Sieve Bronze: Earned 10,000 credits (36,192)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (20,306)TRP Sieve (suspended) Bronze: Earned 10,000 credits (21,738)GFN Bronze: Earned 10,000 credits (86,217)PSA Ruby: Earned 2,000,000 credits (2,143,756)
Message 29958 - Posted: 24 Dec 2010 | 20:21:22 UTC

4-4.5 hours is about right for a prp test at this n level. The ~70 hours is needed for the deterministic test. Since both primary and double check were done with 64 bit (Linux & Windows), I'm not sure how long it would have taken with 32 bit. However, feel free to give it a shot and let us know. :)
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Message 29960 - Posted: 24 Dec 2010 | 20:23:08 UTC - in response to Message 29955.

My guess wouzld be normal tests are finding PRPs. Once a PRP is found, an deterministic test, giving prime or not prime as the result, has to be run. That's what's taking longer then.

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Message 29961 - Posted: 24 Dec 2010 | 20:23:51 UTC - in response to Message 29958.

4-4.5 hours is about right for a prp test at this n level. The ~70 hours is needed for the deterministic test. Since both primary and double check were done with 64 bit (Linux & Windows), I'm not sure how long it would have taken with 32 bit. However, feel free to give it a shot and let us know. :)

Ah, right...I'd forgotten about how the N+1 test would take much longer. (Particularly since it's an N+1...in my experience those generally are much slower than N-1, which in and of itself is slower than the standard PRP test.) Given that, the ~70 hour times would make sense.

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Message boards : News : World Record Primorial Prime

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