533098369554 · 2357# + 3399421667

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:533098369554 · 2357# + 3399421667
Verification status (*):Proven
Official Comment (*):Consecutive primes arithmetic progression (6,d=30), ECPP
Proof-code(s): (*):c98 : Batalov, EMsieve, Primo
Decimal Digits:1012   (log10 is 1011.1020584942)
Rank (*):130516 (digit rank is 21)
Entrance Rank (*):125249
Currently on list? (*):short
Submitted:11/13/2021 23:11:47 UTC
Last modified:5/20/2023 20:59:19 UTC
Database id:132936
Status Flags:none
Score (*):25.3065 (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 1
Subcategory: "Consecutive primes in arithmetic progression (6,d=*)"
(archival tag id 226450, tag last modified 2023-03-11 15:53:59)
Arithmetic Progressions of Primes (archivable class *)
Prime on list: no, rank 941, weight 40.80565409401
Subcategory: "Arithmetic progression (6,d=*)"
(archival tag id 226451, tag last modified 2023-03-11 15:53:59)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 1197
Subcategory: "ECPP"
(archival tag id 226452, tag last modified 2024-06-24 15:37:19)

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.
fieldvalue
prime_id132936
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -tc -hhelper.php?id=1100000002734693832 -q"533098369554*2357#+3399421667" 2>&1
PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8]
Primality testing 533098369554*2357#+3399421667 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000002734693832
Running N-1 test using base 5
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Running N+1 test using discriminant 17, base 3+sqrt(17)
Calling N+1 BLS with factored part 100.00% and helper 1.82% (301.88% proof)


533098369554*2357#+3399421667 is prime! (0.5204s+0.0002s)
[Elapsed time: 0.00 seconds]


Helper File:
2
23
79
281
3297060341051
3
21851
705973
4557533
44172449
180990499
2349649643083
48800921075384570134811
81774827750860851529039092884943566...(942 digits)...90736223263798116245702108496907431
modified2023-03-13 07:27:15
created2023-03-13 07:27:15
id181568

fieldvalue
prime_id132936
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"533098369554*2357#+3399421667" 2>&1 PFGW Version 4.0.1.64BIT.20191203.x86_Dev [GWNUM 29.8] Primality testing 533098369554*2357#+3399421667 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N-1 test using base 11 Running N+1 test using discriminant 17, base 1+sqrt(17) Calling N-1 BLS with factored part 0.57% and helper 0.57% (2.32% proof) 533098369554*2357#+3399421667 is Fermat and Lucas PRP! (0.0655s+0.0001s) [Elapsed time: 0.00 seconds]
modified2022-07-11 18:21:45
created2021-11-13 23:16:03
id178649

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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