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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 (*):||Lucas cofactor, ECPP|
|Unofficial Comments:||This prime has 2 user comments below.|
|Proof-code(s): (*):||c56 : Soule, Minovic, OpenPFGW, Primo|
|Decimal Digits:||9591 (log10 is 9590.9499493164)|
|Rank (*):||81183 (digit rank is 1)|
|Entrance Rank (*):||58526|
|Currently on list? (*):||short|
|Submitted:||3/29/2012 10:37:04 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||32.3106 (normalized score 0)|
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.
- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 313
(archival tag id 214251, tag last modified 2023-03-11 16:02:30)
- Lucas cofactor (archivable *)
- Prime on list: yes, rank 15
Subcategory: "Lucas cofactor"
(archival tag id 214252, tag last modified 2023-03-11 15:53:59)
User comments about this prime (disclaimer):
User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.
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 105913 person_id 9 machine Ditto P4 P4 what prp notes Command: /home/ditto/client/pfgw -tc -q"V(45953)/4561241750239" 2>&1 PFGW Version 126.96.36.199BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing V(45953)/4561241750239 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N+1 test using discriminant 7, base 1+sqrt(7) Calling N+1 BLS with factored part 0.13% and helper 0.08% (0.48% proof) V(45953)/4561241750239 is Fermat and Lucas PRP! (32.4335s+0.0038s) [Elapsed time: 33.00 seconds] modified 2020-07-07 22:30:27 created 2012-03-29 10:38:01 id 141409
field value prime_id 105913 person_id 9 machine RedHat P4 P4 what trial_divided notes Command: /home/caldwell/client/pfgw -o -f -q"V(45953)/4561241750239" 2>&1 PFGW Version 188.8.131.52BIT.20110215.x86_Dev [GWNUM 26.5] V(45953)/4561241750239 1/1 mro=0 trial factoring to 2746508 V(45953)/4561241750239 has no small factor. [Elapsed time: 2.559 seconds] modified 2020-07-07 22:30:27 created 2012-03-29 10:48:51 id 141417
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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