10111725 - 4 · 1055862 - 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: | 10111725 - 4 · 1055862 - 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Near-repdigit, palindrome |
| Proof-code(s): (*): | p235 : Bedwell, OpenPFGW |
| Decimal Digits: | 111725 (log10 is 111725) |
| Rank (*): | 47115 (digit rank is 1) |
| Entrance Rank (*): | 11987 |
| Currently on list? (*): | no |
| Submitted: | 9/4/2010 13:01:43 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 94508 |
| Status Flags: | none |
| Score (*): | 39.8958 (normalized score 0.0053) |
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 106
Subcategory: "Near-repdigit"
(archival tag id 211055, tag last modified 2024-02-07 04:37:20)- Palindrome (archivable *)
- Prime on list: no, rank 68
Subcategory: "Palindrome"
(archival tag id 210836, tag last modified 2024-09-30 12:37:11)
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 94508 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f -q"10^111725-4*10^55862-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] trial factoring to 38373037 10^111725-4*10^55862-1 has no small factor. [Elapsed time: 324.381 seconds] modified 2020-07-07 22:30:33 created 2010-09-04 13:05:01 id 118397
field value prime_id 94508 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -tp -q"10^111725-4*10^55862-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 10^111725-4*10^55862-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 742302 bit request FFT size=(49152,16) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 742302 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 34.95% 10^111725-4*10^55862-1 is prime! (-1622.1419s+0.0200s) [Elapsed time: 3.16 hours] modified 2020-07-07 22:30:33 created 2010-09-04 13:08:01 id 118398
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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