"10000000000000000000...(106961 other digits)...00000000000000000001"
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: | "10000000000000000000...(106961 other digits)...00000000000000000001" |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Tetradic palindrome |
| Proof-code(s): (*): | p235 : Bedwell, OpenPFGW |
| Decimal Digits: | 107001 (log10 is 107000) |
| Rank (*): | 47118 (digit rank is 1) |
| Entrance Rank (*): | 10448 |
| Currently on list? (*): | no |
| Submitted: | 3/15/2010 14:56:33 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Database id: | 92167 |
| Blob database id: | 244 |
| Status Flags: | none |
| Score (*): | 39.7627 (normalized score 0.0053) |
Description: (from blob table id=244)
Discovered with a PFGW script file using a pseudorandom\r\nnumber generator.
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.
- Palindrome (archivable *)
- Prime on list: no, rank 67
Subcategory: "Palindrome"
(archival tag id 210623, tag last modified 2024-01-17 08:37:12)- Tetradic (deprecated *)
- Prime on list: no, rank 5
Subcategory: "Tetradic"
(archival tag id 210624, tag last modified 2023-03-11 15:53:59)
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 92167 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/pfgw -o -f p_92167.txt 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 1000000000...0000000000.........0000000000000000 1/1 trial factoring to 36642684 1000000000...0000000001 has no small factor. [Elapsed time: 1323.897 seconds] modified 2020-07-07 22:30:36 created 2010-03-15 15:05:01 id 113709
field value prime_id 92167 person_id 9 machine Ditto P4 P4 what prime notes Command: /home/ditto/client/pfgw -tc p_92167.txt 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1000000000...0000000001 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 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) 710902 bit request FFT size=(49152,16) Running N-1 test using base 17 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) 710902 bit request FFT size=(49152,16) Running N+1 test using discriminant 23, base 3+sqrt(23) 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) 710910 bit request FFT size=(49152,16) Calling N-1 BLS with factored part 42.15% and helper 0.01% (126.46% proof) 1000000000...0000000001 is prime! (9561.9345s+0.3531s) [Elapsed time: 2.66 hours] modified 2020-07-07 22:30:36 created 2010-03-15 15:08:01 id 113710
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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