10314727 - 8 · 10157363 - 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: | 10314727 - 8 · 10157363 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Near-repdigit, palindrome |
| Proof-code(s): (*): | p235 : Bedwell, OpenPFGW |
| Decimal Digits: | 314727 (log10 is 314727) |
| Rank (*): | 22334 (digit rank is 1) |
| Entrance Rank (*): | 2086 |
| Currently on list? (*): | yes |
| Submitted: | 1/7/2013 23:21:38 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 110658 |
| Status Flags: | none |
| Score (*): | 43.0826 (normalized score 0.1294) |
Archival tags:
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.
- Near-repdigit (archivable *)
- Prime on list: no, rank 47
Subcategory: "Near-repdigit"
(archival tag id 214901, tag last modified 2024-02-07 04:37:20)- Palindrome (archivable *)
- Prime on list: yes, rank 16
Subcategory: "Palindrome"
(archival tag id 214902, tag last modified 2024-08-17 00:37:12)
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.
field value prime_id 110658 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tp -q"10^314727-8*10^157363-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 10^314727-8*10^157363-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^314727-8*10^157363-1 is prime! (46934.4576s+0.0196s) [Elapsed time: 13.04 hours] modified 2020-07-07 22:30:23 created 2013-01-07 23:23:01 id 151591
field value prime_id 110658 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"10^314727-8*10^157363-1" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 10^314727-8*10^157363-1 1/1 mro=0 trial factoring to 115675612 10^314727-8*10^157363-1 has no small factor. [Elapsed time: 2609.883 seconds] modified 2020-07-07 22:30:23 created 2013-01-07 23:35:01 id 151592
Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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