652229318541 · 3527# + 3399421547

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:652229318541 · 3527# + 3399421547
Verification status (*):PRP
Official Comment (*):Consecutive primes arithmetic progression (2,d=30), ECPP
Proof-code(s): (*):c98 : Batalov, EMsieve, Primo
Decimal Digits:1504   (log10 is 1503.1618504971)
Rank (*):104320 (digit rank is 10)
Entrance Rank (*):104289
Currently on list? (*):no
Submitted:10/12/2021 20:36:03 CDT
Last modified:10/12/2021 21:37:18 CDT
Database id:132829
Status Flags:Verify, TrialDiv
Score (*):26.546 (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: no, rank 57
Subcategory: "Consecutive primes in arithmetic progression (2,d=*)"
(archival tag id 226380, tag last modified 2021-10-14 15:37:18)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 898
Subcategory: "Arithmetic progression (2,d=*)"
(archival tag id 226381, tag last modified 2021-10-14 15:37:17)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 885
Subcategory: "ECPP"
(archival tag id 226382, tag last modified 2021-10-14 15:37:18)

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.
machineUsing: Xeon (pool) 4c+4c 3.5GHz
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"652229318541*3527#+3399421547" 2>&1
PFGW Version [GWNUM 29.8]
Primality testing 652229318541*3527#+3399421547 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 5+sqrt(5)
Calling N-1 BLS with factored part 0.54% and helper 0.04% (1.72% proof)

652229318541*3527#+3399421547 is Fermat and Lucas PRP! (0.1337s+0.0004s)
[Elapsed time: 0.00 seconds]
modified2021-10-12 20:41:02
created2021-10-12 20:41:02

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
Printed from the PrimePages <primes.utm.edu> © Chris Caldwell.