45132842379618 · 10255848 - 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:45132842379618 · 10255848 - 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p313 : Broadhurst, Srsieve, OpenPFGW
Decimal Digits:255862   (log10 is 255861.65449269)
Rank (*):26043 (digit rank is 1)
Entrance Rank (*):1062
Currently on list? (*):no
Submitted:2/4/2011 17:33:00 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):9/13/2012 02:15:04 UTC
Database id:97994
Status Flags:none
Score (*):42.446 (normalized score 0.0772)

User comments about this prime (disclaimer):

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David Broadhurst writes (11 Sep 2014):  (report abuse)
45132842379618*10^n-1 is prime for 64 values of n < 256000, namely for n = 1, 5, 7, 10, 13, 14, 16, 21, 22, 37, 41, 51, 55, 60, 63, 82, 84, 90, 96, 105, 119, 165, 176, 197, 223, 247, 292, 307, 312, 314, 339, 356, 511, 554, 1098, 1247, 1772, 2801, 3219, 3423, 3960, 4085, 5878, 6562, 7667, 8650, 8981, 18907, 20740, 25622, 27748, 29703, 31835, 35890, 60533, 79715, 113231, 140934, 172380, 173121, 218810, 225030, 229204, 255848

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_id97994
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 45132842379618 10 255848 -1 2>&1 [Elapsed time: 9.305 seconds]
modified2020-07-07 22:30:32
created2011-02-04 17:35:02
id125377

fieldvalue
prime_id97994
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"45132842379618*10^255848-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 45132842379618*10^255848-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) Reduced from FFT(114688,17) to FFT(114688,16) 1699926 bit request FFT size=(114688,16) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(114688,20) to FFT(114688,19) Reduced from FFT(114688,19) to FFT(114688,18) Reduced from FFT(114688,18) to FFT(114688,17) Reduced from FFT(114688,17) to FFT(114688,16) 1699926 bit request FFT size=(114688,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.89% 45132842379618*10^255848-1 is prime! (-1850.3767s+0.0400s) [Elapsed time: 19.01 hours]
modified2020-07-07 22:30:32
created2011-02-04 17:38:02
id125378

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