1381595338887690358821474589959638055848096769928148782339849168699728696005036217596639028980911635464344630906955931847649826418753025466730960\
47093511481998019892105889132464543550102310865144\
502037206654116795191514099734330521220120978407024096 + 1

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.

Description:1381595338887690358821474589959638055848096769928148782339849168699728696005036217596639028980911635464344630906955931847649826418753025466730960\
47093511481998019892105889132464543550102310865144\
502037206654116795191514099734330521220120978407024096 + 1
Verification status (*):PRP
Official Comment (*):Generalized Fermat
Unofficial Comments:This prime has 2 user comments below.
Proof-code(s): (*):p417 : Tennant, LLR2, PrivGfnServer, OpenPFGW
Decimal Digits:1000000   (log10 is 999999)
Rank (*):1141 (digit rank is 16)
Entrance Rank (*):1080
Currently on list? (*):short
Submitted:8/3/2021 07:15:53 CDT
Last modified:8/4/2021 18:37:17 CDT
Database id:132584
Status Flags:Verify, TrialDiv
Score (*):46.633 (normalized score 8.9222)

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.
Generalized Fermat (archivable *)
Prime on list: no, rank 332
Subcategory: "Generalized Fermat"
(archival tag id 226240, tag last modified 2021-10-13 03:37:17)

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.

Jeppe Stig Nielsen writes (8 Aug 2021):  (report abuse)
Can be written more compactly as:
(floor(10^(999999/4096)) + 102244)^4096 + 1

Private GFN server writes (3 Aug 2021):  (report abuse)
Base factorized with YAFU (ECM mode). To prove as prime, use PFGW factor helper file:
2
3
11
3319
39002209166721466412601474313
1617113357176347987687158483816722519839965209366896732663118910962085884716791519697422593784916876395804427020623351155276729410861198155002747598147793300874034183040243626290783089470092989022566928882860401

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_id132584
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesPFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 1381595338...2097840702^4096+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N-1 test using base 7
Running N-1 test using base 23
Running N-1 test using base 29
Running N-1 test using base 37
Calling Brillhart-Lehmer-Selfridge with factored part 2.19%


1381595338...2097840702^4096+1 is PRP! (125799.0939s+0.0117s)
[Elapsed time: 34.94 hours]
modified2021-08-04 18:12:40
created2021-08-03 07:16:01
id178296

Query times: 0.0006 seconds to select prime, 0.0009 seconds to seek comments.
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