80284312131072 + 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:||80284312131072 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Fermat|
|Proof-code(s): (*):||L5051 : Veit, GFNSvCUDA, GeneFer, AthGFNSieve, PrimeGrid, LLR|
|Decimal Digits:||1036076 (log10 is 1036075.753802)|
|Rank (*):||1335 (digit rank is 1)|
|Entrance Rank (*):||433|
|Currently on list? (*):||short|
|Submitted:||11/17/2020 19:58:23 UTC|
|Last modified:||5/20/2023 20:59:19 UTC|
|Score (*):||46.7417 (normalized score 7.0578)|
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 542
Subcategory: "Generalized Fermat"
(archival tag id 225718, tag last modified 2023-06-03 04:37:21)
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 131406 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"80284312^131072+1" 2>&1 PFGW Version 188.8.131.52BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 80284312^131072+1 [N-1, Brillhart-Lehmer-Selfridge] F: 80284312^131072+1 57344/10907928 (trial factor to 409508040) F: 80284312^131072+1 116736/10907928 (trial factor to 409508040) F: 80284312^131072+1 178176/10907928 (trial factor to 409508040) F: 80284312^131072+1 239616/10907928 (trial factor to 409508040) F: 80284312^131072+1 299008/10907928 (trial factor to 409508040) Running N-1 test using base 3 Calling Brillhart-Lehmer-Selfridge with factored part 88.58% 80284312^131072+1 is prime! (28811.7391s+0.0108s) [Elapsed time: 8.00 hours] modified 2021-04-20 22:39:26 created 2020-11-17 20:01:02 id 177099
Query times: 0.0035 seconds to select prime, 0.0007 seconds to seek comments.
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