7853 · 21321037 + 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.

This prime's information:

Description:7853 · 21321037 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L4097 : Kaczala, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:397676   (log10 is 397675.65741756)
Rank (*):14023 (digit rank is 1)
Entrance Rank (*):2313
Currently on list? (*):no
Submitted:3/9/2015 22:21:21 UTC
Last modified:5/20/2023 20:59:19 UTC
Removed (*):2/16/2018 16:26:04 UTC
Database id:119528
Status Flags:none
Score (*):43.8016 (normalized score 0.3117)

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_id119528
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/client/pfgw/pfgw64 -t -q"7853*2^1321037+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 7853*2^1321037+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 7853*2^1321037+1 is prime! (659.7131s+0.0006s) [Elapsed time: 11.00 minutes]
modified2020-07-07 22:30:17
created2015-03-09 22:31:01
id165137

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