98035 · 10196070 + 1

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:98035 · 10196070 + 1
Verification status (*):Proven
Official Comment (*):Generalized Cullen
Proof-code(s): (*):g157 : Loeh, Proth.exe
Decimal Digits:196075   (log10 is 196074.99138115)
Rank (*):34997 (digit rank is 1)
Entrance Rank (*):479
Currently on list? (*):no
Submitted:2/28/2007 13:25:12 UTC
Last modified:3/11/2023 15:54:10 UTC
Database id:79539
Status Flags:none
Score (*):41.6273 (normalized score 0.0341)

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.
Generalized Cullen (archivable *)
Prime on list: no, rank 65
Subcategory: "Generalized Cullen"
(archival tag id 187277, tag last modified 2023-12-29 19:37:13)

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/TrialDiv/TrialDiv -q 98035 10 196070 1 2>&1 [Elapsed time: 9.530 seconds]
modified2020-07-07 22:30:41
created2007-02-28 13:52:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"98035*10^196070+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 98035*10^196070+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(81920,20) to FFT(81920,19) Reduced from FFT(81920,19) to FFT(81920,18) Reduced from FFT(81920,18) to FFT(81920,17) Reduced from FFT(81920,17) to FFT(81920,16) 1302704 bit request FFT size=(81920,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.90% 98035*10^196070+1 is prime! (5538.9333s+0.0265s) [Elapsed time: 5539 seconds]
modified2020-07-07 22:30:41
created2007-02-28 13:53:01

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