825 · 21504415 - 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:825 · 21504415 - 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1817 : Barnes, PSieve, Srsieve, NPLB, LLR
Decimal Digits:452877   (log10 is 452876.95738078)
Rank (*):9722 (digit rank is 1)
Entrance Rank (*):2715
Currently on list? (*):no
Submitted:4/5/2018 04:22:05 UTC
Last modified:5/20/2023 20:59:19 UTC
Removed (*):8/24/2020 01:11:57 UTC
Database id:124568
Status Flags:none
Score (*):44.201 (normalized score 0.5563)

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 -tp -q"825*2^1504415-1" 2>&1 PFGW Version [GWNUM 27.11] Primality testing 825*2^1504415-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 7, base 1+sqrt(7) Detected in MAXERR>0.45 (round off check) in Exponentiator::Iterate Iteration: 17/1504426 ERROR: ROUND OFF 0.5>0.45 (Test aborted, try again using the -a1 switch) Running N+1 test using discriminant 7, base 1+sqrt(7) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 825*2^1504415-1 is prime! (2927.5147s+0.0007s) [Elapsed time: 48.78 minutes]
modified2020-07-07 22:30:15
created2018-04-05 04:23:01

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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