Phi(2685, 67588246166904)/(72171843001561 · 182332981 · 1923646771 · 174457892355841 · 21784054190313871)

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:Phi(2685, 67588246166904)/(72171843001561 · 182332981 · 1923646771 · 174457892355841 · 21784054190313871)
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c54 : Wu_T, Primo
Decimal Digits:19632   (log10 is 19631.75336861)
Rank (*):71581 (digit rank is 5)
Entrance Rank (*):59838
Currently on list? (*):no
Submitted:3/9/2015 05:58:46 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:119520
Status Flags:Verify, TrialDiv
Score (*):34.5288 (normalized score 0)

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: no, rank 76
Subcategory: "ECPP"
(archival tag id 217916, tag last modified 2023-03-11 16:02:30)

User comments about this prime (disclaimer):

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Tom Wu writes (26 Mar 2015):  (report abuse)
This prime is a helper for the N-1 primality proof of the GRU prime Phi(16111,40734), and can also be expressed as Phi(8055,40734)/(612181*117892981*182332981*1923646771*174457892355841*21784054190313871).

The Primo certificate is available from

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.
machineUsing: Xeon 4c+4c 3.5GHz
notesPFGW Version [GWNUM 27.11] Primality testing Phi(2685,67588246166904)/(72171843001561*182332981*1923646771*174457892355841*21784054190313871) [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 13 Running N+1 test using discriminant 19, base 9+sqrt(19) Calling N-1 BLS with factored part 0.05% and helper 0.00% (0.15% proof) Phi(2685,67588246166904)/(72171843001561*182332981*1923646771*174457892355841*21784054190313871) is Fermat and Lucas PRP! (32.6892s+0.0011s) [Elapsed time: 32.00 seconds]
modified2020-07-07 22:30:17
created2015-03-09 06:11:02

Query times: 0.0005 seconds to select prime, 0.005 seconds to seek comments.
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