" - τ(3312128)"
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.
This prime's information:
|Description:||" - τ(3312128)"|
|Verification status (*):||PRP|
|Official Comment (*):||ECPP|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||c80 : Lygeros, Rozier, Anonymous, Primo|
|Decimal Digits:||29492 (log10 is 29491.63071975)|
|Rank (*):||68718 (digit rank is 1)|
|Entrance Rank (*):||57016|
|Currently on list? (*):||no|
|Submitted:||9/16/2015 19:21:34 UTC|
|Last modified:||5/20/2023 20:59:19 UTC|
|Blob database id:||349|
|Score (*):||35.7869 (normalized score 0.0001)|
Description: (from blob table id=349)
Lehmer - Ramanujan(331,2129), 29492 decimal digits. Certified by Philippe Alsina, Pierre Gazzano, Nik Lygeros, Olivier Rozier and André Solaris (EU, 2015). The proof took 18 months using a bi - Xeon. Certificate: ecpp29492.7z.001 (12.3 MB) ecpp29492.7z.002 (12.3 MB) ecpp29492.7z.003 (10.6 MB)
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
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The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions. We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.
field value prime_id 120374 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes PFGW Version 184.108.40.206BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 4272870686...2041256991 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 11 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N+1 BLS with factored part 0.06% and helper 0.03% (0.20% proof) 4272870686...2041256991 is Fermat and Lucas PRP! (77.4215s+0.0127s) [Elapsed time: 78.00 seconds] modified 2020-07-07 22:30:17 created 2015-09-16 19:27:02 id 166002