R(1031)

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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:	R(1031)
Verification status (*):	Proven
Official Comment (*):	Repunit
Proof-code(s): (*):	WD : Williams, Dubner, Cruncher
Decimal Digits:	1031 (log₁₀ is 1030.0457574906)
Rank (*):	127683 (digit rank is 57)
Entrance Rank (*):	565
Currently on list? (*):	yes
Submitted:	1985
Last modified:	3/11/2023 15:54:10 UTC
Database id:	55968
Status Flags:	none
Score (*):	25.3646 (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.

Repunit (archivable *)
Prime on list: yes, rank 3
Subcategory: "Repunit"
(archival tag id 186344, tag last modified 2023-05-15 15:37:15)

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 55968

person_id 9

machine RedHat P4 P4

what prime

notes Command: /home/caldwell/client/pfgw -tc -hhelp1031 -q"R(1031)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing R(1031) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file help1031 Running N-1 test using base 7 Running N+1 test using discriminant 29, base 2+sqrt(29) Calling N-1 BLS with factored part 40.49% and helper 0.09% (121.60% proof) R(1031) is prime! (0.4723s+0.0003s) [Elapsed time: 0.00 seconds] Helper File: 7034077 Phi(103,10)/1031/7034077 44092859 102860539 984385009 612053256358933 182725114866521155647161 Phi(206,10)/1237/44092859/102860539/984385009/612053256358933/182725114866521155647161 5905014721 326345481191 2702394989404991 7073532436575439739956079653594194521 85517237338860102283865323577960208481 497491 569836171 2013681931 567664121498896654896380203841 896048585318577702680084550566846611

modified 2020-07-07 22:30:31

created 2011-03-31 02:56:24

id 128098

field	value
prime_id	55968
person_id	9
machine	RedHat P4 P4
what	prime
notes	Command: /home/caldwell/client/pfgw -tc -hhelp1031 -q"R(1031)" 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing R(1031) [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file help1031 Running N-1 test using base 7 Running N+1 test using discriminant 29, base 2+sqrt(29) Calling N-1 BLS with factored part 40.49% and helper 0.09% (121.60% proof) R(1031) is prime! (0.4723s+0.0003s) [Elapsed time: 0.00 seconds] Helper File: 7034077 Phi(103,10)/1031/7034077 44092859 102860539 984385009 612053256358933 182725114866521155647161 Phi(206,10)/1237/44092859/102860539/984385009/612053256358933/182725114866521155647161 5905014721 326345481191 2702394989404991 7073532436575439739956079653594194521 85517237338860102283865323577960208481 497491 569836171 2013681931 567664121498896654896380203841 896048585318577702680084550566846611
modified	2020-07-07 22:30:31
created	2011-03-31 02:56:24
id	128098

Query times: 0.0002 seconds to select prime, 0.0006 seconds to seek comments.