993530619517 · 2503# + 1633050373

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:993530619517 · 2503# + 1633050373
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (5,d=30)
Proof-code(s): (*):x38 : Broadhurst, OpenPFGW, Primo
Decimal Digits:1073   (log10 is 1072.2958888695)
Rank (*):119709 (digit rank is 28)
Entrance Rank (*):103813
Currently on list? (*):short
Submitted:12/19/2013 23:43:49 CDT
Last modified:12/20/2013 00:20:55 CDT
Database id:116682
Status Flags:Verify, TrialDiv
Score (*):25.4903 (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.
Consecutive Primes in Arithmetic Progression (archivable class *)
Prime on list: yes, rank 5
Subcategory: "Consecutive primes in arithmetic progression (5,d=*)"
(archival tag id 217532, tag last modified 2021-10-12 21:37:20)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 735, weight 37.535786789796
Subcategory: "Arithmetic progression (5,d=*)"
(archival tag id 217533, tag last modified 2021-10-12 21:37:20)

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -tc -q"993530619517*2503#+1633050373" 2>&1 PFGW Version [GWNUM 26.5] Primality testing 993530619517*2503#+1633050373 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 3 Running N+1 test using discriminant 11, base 1+sqrt(11) Calling N-1 BLS with factored part 0.51% and helper 0.22% (1.77% proof) 993530619517*2503#+1633050373 is Fermat and Lucas PRP! (0.4170s+0.0003s) [Elapsed time: 0.00 seconds]
modified2020-07-07 17:30:18
created2013-12-19 23:53:04

Query times: 0.0005 seconds to select prime, 0.0005 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.