4095 · 2504896 + 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.

Description:4095 · 2504896 + 1
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):L1287 : Naas, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:151993   (log10 is 151992.45294467)
Rank (*):34472 (digit rank is 1)
Entrance Rank (*):4866
Currently on list? (*):no
Submitted:5/12/2010 14:13:38 CDT
Last modified:5/12/2010 14:50:23 CDT
Removed (*):5/23/2010 15:47:18 CDT
Database id:92656
Status Flags:none
Score (*):40.8436 (normalized score 0.0348)

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_id92656
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 4095 2 504896 1 2>&1 [Elapsed time: 9.219 seconds]
modified2020-07-07 17:30:35
created2010-05-12 14:18:02
id114686

fieldvalue
prime_id92656
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"4095*2^504896+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4095*2^504896+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1009824 bit request FFT size=(65536,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 4095*2^504896+1 is prime! (1331.7100s+0.0000s) [Elapsed time: 22.23 minutes]
modified2020-07-07 17:30:35
created2010-05-12 14:23:02
id114690

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