215317227 + 27658614 + 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.
|Description:||215317227 + 27658614 + 1|
|Verification status (*):||Proven|
|Official Comment (*):||Gaussian Mersenne norm 41?, generalized unique|
|Unofficial Comments:||This prime has 2 user comments below.|
|Proof-code(s): (*):||L5123 : Propper, Batalov, EMsieve, LLR|
|Decimal Digits:||4610945 (log10 is 4610944.7773942)|
|Rank (*):||31 (digit rank is 1)|
|Entrance Rank (*):||20|
|Currently on list? (*):||short|
|Submitted:||7/31/2020 16:56:46 CDT|
|Last modified:||8/9/2020 09:31:50 CDT|
|Score (*):||51.3175 (normalized score 842.7613)|
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.
- Gaussian Mersenne norm (archivable *)
- Prime on list: yes, rank 1
Subcategory: "Gaussian Mersenne norm"
(archival tag id 224076, tag last modified 2020-08-02 20:20:04)
- Generalized Unique (archivable *)
- Prime on list: yes, rank 2
Subcategory: "Generalized Unique"
(archival tag id 224078, tag last modified 2020-08-04 13:50:04)
User comments about this prime (disclaimer):
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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 131043 person_id 9 machine Using: Xeon 4c+4c 3.5GHz what prime notes Command: /home/caldwell/client/pfgw/pfgw64 -t -q"2^15317227+2^7658614+1" 2>&1 PFGW Version 18.104.22.168BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 2^15317227+2^7658614+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Calling Brillhart-Lehmer-Selfridge with factored part 50.00% 2^15317227+2^7658614+1 is prime! (750648.5746s+0.0068s) [Elapsed time: 8.69 days] modified 2021-04-20 17:39:26 created 2020-07-31 17:01:01 id 176731