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:
|Verification status (*):||PRP|
|Official Comment (*):||[none]|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p414 : Naimi, OpenPFGW|
|Decimal Digits:||587124 (log10 is 587123.77389594)|
|Rank (*):||3542 (digit rank is 1)|
|Entrance Rank (*):||2273|
|Currently on list? (*):||yes|
|Submitted:||11/30/2020 20:57:53 CDT|
|Last modified:||12/1/2020 09:20:19 CDT|
|Blob database id:||391|
|Status Flags:||Verify, TrialDiv|
|Score (*):||44.9984 (normalized score 1.4395)|
Description: (from blob table id=391)
This Prime is obtained by iteration of the following PARI/GP code: k = [1, 1, 1, 2, 5, 9, 6, 79, 16, 219, 580, 387, 189, 7067, 1803, 6582, 31917, 18888, 20973, 132755, 11419]; q = 2; for(i=1, #k, q = k[i] * (q - 1) * q + 1); print("n",q,"n"); Every Prime in these iterations (including the P587124) are verified to be prime via PFGW using " - tc" flag and then added to the helper file to prove the primality of the next iteration. Every prime q in these iterations can be proven via N - 1 method since all the prime factors of q - 1 are known
User comments about this prime (disclaimer):
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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.
field value prime_id 131431 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prp notes Command: /home/caldwell/client/pfgw/pfgw64 -tc p_131431.txt 2>&1 PFGW Version 188.8.131.52BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 5941497781...4622336001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N-1 test using base 17 Running N+1 test using discriminant 23, base 1+sqrt(23) Calling N-1 BLS with factored part 0.01% and helper 0.00% (0.03% proof) 5941497781...4622336001 is Fermat and Lucas PRP! (43259.4396s+0.8836s) [Elapsed time: 12.02 hours] modified 2021-04-20 17:39:26 created 2020-11-30 21:01:02 id 177124