((sqrtnint(10999999, 2048) + 2) + 364176)2048 + 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:||((sqrtnint(10999999, 2048) + 2) + 364176)2048 + 1|
|Verification status (*):||PRP|
|Official Comment (*):||Generalized Fermat|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p417 : Tennant, LLR2, PrivGfnServer, OpenPFGW|
|Decimal Digits:||1000000 (log10 is 999999)|
|Rank (*):||1399 (digit rank is 4)|
|Entrance Rank (*):||1384|
|Currently on list? (*):||short|
|Submitted:||5/12/2022 06:45:23 CDT|
|Last modified:||5/12/2022 22:37:20 CDT|
|Blob database id:||400|
|Status Flags:||Reparse, Verify, TrialDiv|
|Score (*):||46.633 (normalized score 7.791)|
title='from prime_blob table' id='blob'>Description: (from blob table id=400)
This is GFN - 11 MEGA prime b^2048 + 1, but b is 489 digits long and T5K entries limited to 255 characters. True algebraic representation of the prime:
5825910624014^2048 + 1
The description is in PARI/GP language. sqrtnint(10^999999,2048) + 2 is a minimal value of b required to make number b^2048 + 1 exactly 1,000,000 digits long.
This is a first GFN - 11 MEGA prime. An interesting fact is that 489 - digits base was successfully factorized and number can be proved prime with PFGW. Factorization of the base can be found at http://factordb.com/index.php?id=1100000002986607281
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.
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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 133922 person_id 9 machine Using: Dual Intel Xeon Gold 5222 CPUs 3.8GHz what prp notes Command: /home/caldwell/clientpool/1/pfgw64 -tc p_133922.txt 2>&1
PFGW Version 22.214.171.124BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 1000000000...2022291457 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 31, base 1+sqrt(31)
Calling N-1 BLS with factored part 0.87% and helper 0.00% (2.61% proof)
1000000000...2022291457 is Fermat and Lucas PRP! (56612.7899s+1.9921s)
[Elapsed time: 15.73 hours]
modified 2022-05-12 22:29:36 created 2022-05-12 06:46:01 id 179644