232497 · ((176845 · (79194 · ((97326 · (16182 · ((2988 · (8385 · (81400 · (256084 · (97495 · (40710 · 189295068434802530474023 + 40825)3 + 98124)3 + 257838)3 + 81585)3 + 8386))3 + 1) + 1))3 + 1) + 1))3 + 1) + 1

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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:232497 · ((176845 · (79194 · ((97326 · (16182 · ((2988 · (8385 · (81400 · (256084 · (97495 · (40710 · 189295068434802530474023 + 40825)3 + 98124)3 + 257838)3 + 81585)3 + 8386))3 + 1) + 1))3 + 1) + 1))3 + 1) + 1
Verification status (*):PRP
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p269 : Zhou, OpenPFGW
Decimal Digits:161910   (log10 is 161909.043377)
Rank (*):43400 (digit rank is 1)
Entrance Rank (*):4898
Currently on list? (*):no
Submitted:8/29/2010 12:29:47 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):9/7/2010 20:37:20 UTC
Database id:94439
Status Flags:Verify
Score (*):41.0381 (normalized score 0.0045)

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)
Detail please see:
HERE.

Proving script:
#!/bin/sh
./pfgw -l"pmtup.11.2.cert" -tp p_03
./pfgw -l"pmtup.11.2.cert" -t -h"p_03" ph_04
./pfgw -l"pmtup.11.2.cert" -t -h"ph_04" p_04
./pfgw -l"pmtup.11.2.cert" -t -h"p_04" ph_05
./pfgw -l"pmtup.11.2.cert" -t -h"ph_05" p_05
./pfgw -l"pmtup.11.2.cert" -t -h"p_05" ph_06
./pfgw -l"pmtup.11.2.cert" -t -h"ph_06" p_06
./pfgw -l"pmtup.11.2.cert" -t -h"p_06" ph_07
./pfgw -l"pmtup.11.2.cert" -t -h"ph_07" p_07
./pfgw -l"pmtup.11.2.cert" -t -h"p_07" ph_08
./pfgw -l"pmtup.11.2.cert" -t -h"ph_08" p_08
./pfgw -l"pmtup.11.2.cert" -t -h"p_08" ph_09
./pfgw -l"pmtup.11.2.cert" -t -h"ph_09" p_09
./pfgw -l"pmtup.11.2.cert" -t -h"p_09" ph_10
./pfgw -l"pmtup.11.2.cert" -t -h"ph_10" p_10
./pfgw -l"pmtup.11.2.cert" -t -h"p_10" ph_11
./pfgw -l"pmtup.11.2.cert" -t -h"ph_11" p_11

Helpers:
p_03: 14*2633863^3+15
ph_04: (1036*2633863^3+1110)^2-1036*2633863^3-1109
p_04: 354*(1036*2633863^3+1110)^3+355
ph_05: (40710*(1036*2633863^3+1110)^3+40824)*(40710*(1036*2633863^3+1110)^3+40825)+1
p_05: 155*(40710*(1036*2633863^3+1110)^3+40825)^3+156
ph_06: (97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98123)*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)+1
p_06: 146*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+147
ph_07: (256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257837)*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)+1
p_07: 440*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+441
ph_08: (81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81584)*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)+1
p_08: 8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386
ph_09: ((50108760*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+50114735)^2+3)/4
p_09: 16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1
ph_10: ((194652*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1)-1)^2+3)/4
p_10: 79194*((97326*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1))^3+1)+1
ph_11: ((353690*(79194*((97326*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1))^3+1)+1)-1)^2+3)/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_id94439
person_id9
machineDitto P4 P4
whattrial_divided
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] 232497*((176845*(79194*((.........^3+1)+1))^3+1)+1 1/1 trial factoring to 57006047 232497*((176845*(79194*((97326*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1))^3+1)+1))^3+1)+1 has no small factor. [Elapsed time: 683.985 seconds]
modified2020-07-07 22:30:33
created2010-08-29 12:35:01
id118260

fieldvalue
prime_id94439
person_id9
machineDitto P4 P4
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 232497*((176845*(79194*((97326*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1))^3+1)+1))^3+1)+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 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) 1075710 bit request FFT size=(65536,17) Calling Brillhart-Lehmer-Selfridge with factored part 0.01% 232497*((176845*(79194*((97326*(16182*((2988*(8385*(81400*(256084*(97495*(40710*(1036*2633863^3+1110)^3+40825)^3+98124)^3+257838)^3+81585)^3+8386))^3+1)+1))^3+1)+1))^3+1)+1 is PRP! (-330.0173s+0.0500s) [Elapsed time: 66.53 minutes]
modified2020-07-07 22:30:33
created2010-08-29 12:38:01
id118261

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