51456836560 · 5303# + 1

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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:	51456836560 · 5303# + 1
Verification status (*):	Proven
Official Comment (*):	Arithmetic progression (1,d=10892863626*5303#)
Proof-code(s): (*):	p406 : DavisK, Luhn, Underwood, NewPGen, PrimeForm_egroup, OpenPFGW
Decimal Digits:	2271 (log₁₀ is 2270.0271420716)
Rank (*):	103736 (digit rank is 2985)
Entrance Rank (*):	95057
Currently on list? (*):	no
Submitted:	8/19/2019 13:51:55 UTC
Last modified:	5/20/2023 20:59:19 UTC
Database id:	129871
Status Flags:	none
Score (*):	27.832 (normalized score 0)

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.

Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 772
Subcategory: "Arithmetic progression (1,d=*)"
(archival tag id 223509, tag last modified 2024-06-28 08:37:18)

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 129871

person_id 9

machine Using: Xeon (pool) 4c+4c 3.5GHz

what prime

notes Command: /home/caldwell/clientpool/1/pfgw64 -t -q"51456836560*5303#+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 51456836560*5303#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5333 Calling Brillhart-Lehmer-Selfridge with factored part 33.44% 51456836560*5303#+1 is prime! (0.7591s+0.0008s) [Elapsed time: 1.00 seconds]

modified 2020-07-07 22:30:11

created 2019-08-19 13:53:02

id 175536

field	value
prime_id	129871
person_id	9
machine	Using: Xeon (pool) 4c+4c 3.5GHz
what	prime
notes	Command: /home/caldwell/clientpool/1/pfgw64 -t -q"514568365605303#+1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 514568365605303#+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5333 Calling Brillhart-Lehmer-Selfridge with factored part 33.44% 51456836560*5303#+1 is prime! (0.7591s+0.0008s) [Elapsed time: 1.00 seconds]
modified	2020-07-07 22:30:11
created	2019-08-19 13:53:02
id	175536

Query times: 0.0002 seconds to select prime, 0.0002 seconds to seek comments.