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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 (*):||Fibonacci cofactor, ECPP|
|Proof-code(s): (*):||c8 : Broadhurst, Water, Primo|
|Decimal Digits:||7213 (log10 is 7212.968891043)|
|Rank (*):||84207 (digit rank is 1)|
|Entrance Rank (*):||67325|
|Currently on list? (*):||short|
|Submitted:||7/1/2013 14:01:19 UTC|
|Last modified:||3/11/2023 15:54:10 UTC|
|Score (*):||31.4269 (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 407
(archival tag id 217196, tag last modified 2023-03-11 16:02:30)
- Fibonacci cofactor (archivable *)
- Prime on list: yes, rank 20
Subcategory: "Fibonacci cofactor"
(archival tag id 217197, tag last modified 2023-03-11 15:53:59)
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 114542 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"U(34607)/13088506284255296513" 2>&1 PFGW Version 126.96.36.199BIT.20110215.x86_Dev [GWNUM 26.5] U(34607)/13088506284255296513 1/1 mro=0 trial factoring to 2017693 U(34607)/13088506284255296513 has no small factor. [Elapsed time: 1.800 seconds] modified 2020-07-07 22:30:19 created 2013-07-01 14:05:02 id 159462
field value prime_id 114542 person_id 9 machine WinXP Dual Core 2.6GHz 32-bit what prp notes Command: pfgw32.exe -tc -q"U(34607)/13088506284255296513" 2>&1 PFGW Version 188.8.131.52BIT.20130210.Win_Dev [GWNUM 27.8] Primality testing U(34607)/13088506284255296513 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Calling N-1 BLS with factored part 0.28% and helper 0.20% (1.04% proof) U(34607)/13088506284255296513 is Fermat and Lucas PRP! (15.5675s+0.0028s) [Elapsed time: 17 seconds] modified 2020-07-07 22:30:19 created 2013-07-01 14:30:06 id 159464
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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