4 · 10103958 + 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: | 4 · 10103958 + 1 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Generalized Fermat |
| Proof-code(s): (*): | g375 : Benson, NewPGen, OpenPFGW, Proth.exe |
| Decimal Digits: | 103959 (log10 is 103958.60206) |
| Rank (*): | 48257 (digit rank is 1) |
| Entrance Rank (*): | 654 |
| Currently on list? (*): | no |
| Submitted: | 12/31/2004 09:46:19 UTC |
| Last modified: | 3/11/2023 15:54:10 UTC |
| Removed (*): | 11/29/2008 02:50:20 UTC |
| Database id: | 72946 |
| Status Flags: | none |
| Score (*): | 39.6738 (normalized score 0.0042) |
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.
- Generalized Fermat (archivable *)
- Prime on list: no, rank 4921
Subcategory: "Generalized Fermat"
(archival tag id 204986, tag last modified 2024-11-22 05:37:10)
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 72946 person_id 9 machine Linux P4 2.8GHz what prime notes Command: /home/caldwell/client/pfgw -f -t -q"4*10^103958+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4*10^103958+1 [N-1, Brillhart-Lehmer-Selfridge] trial factoring to 35531467 Running N-1 test using base 3 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) 690696 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.90% 4*10^103958+1 is prime! (2124.3900s+0.0100s) modified 2020-07-07 22:30:45 created 2004-12-31 10:11:09 id 77951
Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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