" - τ(3312128)"
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:

field (help)value
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 (*):60342 (digit rank is 1)
Entrance Rank (*):57016
Currently on list? (*):short
Submitted:9/16/2015 14:21:34 CDT
Last modified:9/16/2015 14:48:34 CDT
Database id:120374
Blob database id:349
Status Flags:Verify, TrialDiv
Score (*):35.7869 (normalized score 0.0003)

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)

Archival tags:

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.
Elliptic Curve Primality Proof (archivable *)
Prime on list: yes, rank 4
Subcategory: "ECPP"
(archival tag id 218079, tag last modified 2017-11-16 23:50:19)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (16 Sep 2015): 
-U(63584021925868,331^11,2129)

Verification data:

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.
fieldvalue
prime_id120374
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesPFGW Version 3.7.7.64BIT.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]
modified2016-04-08 12:40:28
created2015-09-16 14:27:02
id166002

Query times: 0.0002 seconds to select prime, 0.0001 seconds to seek comments.