(((((((((((((((((((((((((8423163161706505305132 - 47)/2)2 - 3575)/2)2 - 2903)/2)2 - 194223)/2)2 - 16671)/2)2 - 70411)/2)2 - 946843)/2)2 - 18907)/2)2 - 62991931)/2)2 - 320282843)/2)2 - 97624131)/2)2 - 25770331)/2)2 - 90011400365)/4

Previous Next Random

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:(((((((((((((((((((((((((8423163161706505305132 - 47)/2)2 - 3575)/2)2 - 2903)/2)2 - 194223)/2)2 - 16671)/2)2 - 70411)/2)2 - 946843)/2)2 - 18907)/2)2 - 62991931)/2)2 - 320282843)/2)2 - 97624131)/2)2 - 25770331)/2)2 - 90011400365)/4
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p269 : Zhou, OpenPFGW
Decimal Digits:168956   (log10 is 168955.45522301)
Rank (*):42343 (digit rank is 2)
Entrance Rank (*):4314
Currently on list? (*):no
Submitted:9/6/2010 11:52:25 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):10/23/2010 08:59:33 UTC
Database id:94526
Status Flags:none
Score (*):41.1692 (normalized score 0.0051)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Lei Zhou writes (11 Sep 2014):  (report abuse)
The certificate can be found HERE.

Proving code:
#!/bin/sh
./pfgw -l"pmdance.21.cert" -t p_07
./pfgw -l"pmdance.21.cert" -t -h"p_07" p_08
./pfgw -l"pmdance.21.cert" -t -h"p_08" p_09
./pfgw -l"pmdance.21.cert" -tp -h"p_09" p_10
./pfgw -l"pmdance.21.cert" -t -h"p_10" p_11
./pfgw -l"pmdance.21.cert" -t -h"p_11" p_12
./pfgw -l"pmdance.21.cert" -tp -h"p_12" p_13
./pfgw -l"pmdance.21.cert" -t -h"p_13" p_14
./pfgw -l"pmdance.21.cert" -tp -h"p_14" p_15
./pfgw -l"pmdance.21.cert" -tp -h"p_15" p_16
./pfgw -l"pmdance.21.cert" -tp -h"p_16" p_17
./pfgw -l"pmdance.21.cert" -t -h"p_17" p_18
./pfgw -l"pmdance.21.cert" -tp -h"p_18" p_19
./pfgw -l"pmdance.21.cert" -tp -h"p_19" p_20
./pfgw -l"pmdance.21.cert" -tp -h"p_20" p_21

Helpers:
p_07: 20522138249
p_08: 421158158085325265263
p_09: (842316316170650530513^2-165)/4
p_10: (((842316316170650530513^2-47)/2)^2-3485)/4
p_11: (((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2021)/4
p_12: (((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194477)/4
p_13: (((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16133)/4
p_14: (((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-72357)/4
p_15: (((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946733)/4
p_16: (((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-3029)/4
p_17: (((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-63027725)/4
p_18: (((((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320302605)/4
p_19: (((((((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97634165)/4
p_20: (((((((((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97624131)/2)^2-25170293)/4

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_id94526
person_id9
machineDitto P4 P4
whattrial_divided
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (((((((((((((((((((((((((.........0331)/2)^2-90011 1/1 trial factoring to 59654288 (((((((((((((((((((((((((8423163161...0650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97624131)/2)^2-25770331)/2)^2-90011400365)/4 has no small factor. [Elapsed time: 745.599 seconds]
modified2020-07-07 22:30:33
created2010-09-06 12:05:02
id118435

fieldvalue
prime_id94526
person_id9
machineRedHat Virtual STEM Server
whatprime
notesPFGW Version 3.3.4.20100405.x86_Stable [GWNUM 25.14] Primality testing (((((((((((((((((((((((((8423163161...0650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97624131)/2)^2-25770331)/2)^2-90011400365)/4 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper Prime_Testing_Warning, unused factor from helper file: 20522138249 Running N-1 test using base 2 Running N-1 test using base 7 Running N+1 test using discriminant 13, base 8+sqrt(13) Running N+1 test using discriminant 13, base 9+sqrt(13) Calling N+1 BLS with factored part 50.00% and helper 0.01% (150.01% proof) (((((((((((((((((((((((((8423163161...0650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97624131)/2)^2-25770331)/2)^2-90011400365)/4 is prime! (17763.0182s+0.1020s) [Elapsed time: 4.94 hours] Helper File: 20522138249 421158158085325265263 (842316316170650530513^2-165)/4 (((842316316170650530513^2-47)/2)^2-3485)/4 (((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2021)/4 (((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194477)/4 (((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16133)/4 (((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-72357)/4 (((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946733)/4 (((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-3029)/4 (((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-63027725)/4 (((((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320302605)/4 (((((((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97634165)/4 (((((((((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97624131)/2)^2-25170293)/4 (((((((((((((((((((((((((842316316170650530513^2-47)/2)^2-3575)/2)^2-2903)/2)^2-194223)/2)^2-16671)/2)^2-70411)/2)^2-946843)/2)^2-18907)/2)^2-62991931)/2)^2-320282843)/2)^2-97624131)/2)^2-25770331)/2
modified2020-07-07 22:30:33
created2010-11-28 03:32:32
id122618

Query times: 0.0004 seconds to select prime, 0.0003 seconds to seek comments.
Printed from the PrimePages <t5k.org> © Reginald McLean.