3428602715439 · 235678 + 13

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:3428602715439 · 235678 + 13
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (3,d=6), ECPP
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):c93 : Batalov, PolySieve, Primo
Decimal Digits:10753   (log10 is 10752.683302464)
Rank (*):82359 (digit rank is 1)
Entrance Rank (*):75203
Currently on list? (*):short
Submitted:4/25/2020 01:54:01 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:130856
Status Flags:Verify
Score (*):32.665 (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.
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: yes, rank 3
Subcategory: "Consecutive primes in arithmetic progression (3,d=*)"
(archival tag id 223974, tag last modified 2023-03-11 15:53:59)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 136, weight 38.277720988461
Subcategory: "Arithmetic progression (3,d=*)"
(archival tag id 223975, tag last modified 2023-03-11 16:02:30)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 281
Subcategory: "ECPP"
(archival tag id 223976, tag last modified 2024-04-24 05:37:25)

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.

Serge Batalov writes (25 Apr 2020):  (report abuse)
Certificate is at FactorDB

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 (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"3428602715439*2^35678+13" 2>&1 PFGW Version [GWNUM 29.8] Primality testing 3428602715439*2^35678+13 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N+1 BLS with factored part 0.10% and helper 0.03% (0.34% proof) 3428602715439*2^35678+13 is Fermat and Lucas PRP! (2.7906s+0.0001s) [Elapsed time: 3.00 seconds]
modified2020-07-07 22:30:10
created2020-04-25 01:56:05

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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