45132842379618 · 10218810 - 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 · 10218810 - 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:218824   (log10 is 218823.65449269)
Rank (*):29127 (digit rank is 1)
Entrance Rank (*):1877
Currently on list? (*):no
Submitted:1/27/2011 02:27:40 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):3/18/2012 21:43:38 UTC
Database id:97764
Status Flags:none
Score (*):41.965 (normalized score 0.0496)

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 61 values of n < 219000, 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

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_id97764
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 45132842379618 10 218810 -1 2>&1 [Elapsed time: 9.531 seconds]
modified2020-07-07 22:30:32
created2011-01-27 02:35:02
id124917

fieldvalue
prime_id97764
person_id9
machineRedHat Virtual STEM Server
whatprime
notesCommand: /home/caldwell/client/pfgw -tp -q"45132842379618*10^218810-1" 2>&1 PFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing 45132842379618*10^218810-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 11, base 1+sqrt(11) Calling Brillhart-Lehmer-Selfridge with factored part 69.89% 45132842379618*10^218810-1 is prime! (10078.6761s+0.0510s) [Elapsed time: 2.80 hours]
modified2020-07-07 22:30:32
created2011-01-27 02:50:48
id124918

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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