26858122665536 + 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:||26858122665536 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Proof-code(s): (*):||L5654 : DeJesus, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR|
|Decimal Digits:||552408 (log10 is 552407.90192493)|
|Rank (*):||4623 (digit rank is 1)|
|Entrance Rank (*):||4510|
|Currently on list? (*):||yes|
|Submitted:||5/1/2023 22:23:52 UTC|
|Last modified:||5/20/2023 20:59:19 UTC|
|Score (*):||44.8112 (normalized score 1.0241)|
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 1045
Subcategory: "Generalized Fermat"
(archival tag id 228533, tag last modified 2023-06-03 15:37:35)
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 136009 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -t -q"268581226^65536+1" 2>&1
PFGW Version 18.104.22.168BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 268581226^65536+1 [N-1, Brillhart-Lehmer-Selfridge]
F: 268581226^65536+1 92160/5807586 (trial factor to 210260125)
F: 268581226^65536+1 174080/5807586 (trial factor to 210260125)
Running N-1 test using base 3
Special modular reduction using generic reduction AVX-512 FFT length 192K, Pass1=192, Pass2=1K, clm=1 on 268581226^65536+1
Calling Brillhart-Lehmer-Selfridge with factored part 81.26%
268581226^65536+1 is prime! (5146.5054s+0.0063s)
[Elapsed time: 85.77 minutes]
modified 2023-05-02 04:13:01 created 2023-05-02 02:47:15 id 181823
Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
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