345535 + 2

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:345535 + 2
Verification status (*):PRP
Official Comment (*):ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c95 : Gelhar, Primo
Decimal Digits:21726   (log10 is 21725.71633366)
Rank (*):72634 (digit rank is 1)
Entrance Rank (*):66006
Currently on list? (*):no
Submitted:6/22/2020 18:33:15 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:130986
Status Flags:Verify
Score (*):34.8422 (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 77
Subcategory: "ECPP"
(archival tag id 224047, tag last modified 2024-03-24 06:37:14)

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.

Robert Gelhar writes (5 Jul 2020):  (report abuse)
http://factordb.com/index.php?id=1100000000213105555 is the id for the certificate for this prime at FactorDB, which has also double checked the certificate.

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_id130986
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"3^45535+2" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 3^45535+2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 2+sqrt(7) Calling N-1 BLS with factored part 0.02% and helper 0.02% (0.09% proof) 3^45535+2 is Fermat and Lucas PRP! (7.0121s+0.0089s) [Elapsed time: 7.00 seconds]
modified2020-07-07 22:30:10
created2020-06-22 18:36:01
id176673

Query times: 0.0003 seconds to select prime, 0.0005 seconds to seek comments.
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