861 · 27895451 - 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:861 · 27895451 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L4965 : Propper, LLR
Decimal Digits:2376771   (log10 is 2376770.5152983)
Rank (*):180 (digit rank is 1)
Entrance Rank (*):89
Currently on list? (*):short
Submitted:2/21/2021 14:34:18 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132018
Status Flags:none
Score (*):49.2876 (normalized score 75.2164)

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_id132018
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/4/pfgw64 -tp -q"861*2^7895451-1" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 861*2^7895451-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 18/7895462 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 19/7895462 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a2 (or possibly -a0) switch) Running N+1 test using discriminant 5, base 1+sqrt(5) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 861*2^7895451-1 is prime! (139564.8744s+0.0020s) [Elapsed time: 1.62 days]
modified2021-04-20 22:39:25
created2021-02-21 14:59:51
id177717

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