23775 - 7

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:23775 - 7
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):F : Forbes
Decimal Digits:1137   (log10 is 1136.3882336315)
Rank (*):125193 (digit rank is 23)
Entrance Rank (*):13763
Currently on list? (*):no
Submitted:5/1996
Last modified:1/28/2026 14:09:32 UTC
Removed (*):5/1996
Database id:50825
Status Flags:none
Score (*):25.6719 (normalized score 0)

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_id50825
person_id9
machineUsing: Digital Ocean Droplet
whatprime
notesCommand: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper.php?id=1100000000294464327 -q"2^3775-7" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 2^3775-7 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper.php?id=1100000000294464327
trial


Running N-1 test using base 19
Special modular reduction using FMA3 FFT length 192 on 2^3775-7
Running N-1 test using base 23
Special modular reduction using FMA3 FFT length 192 on 2^3775-7
Running N+1 test using discriminant 37, base 12+sqrt(37)
Special modular reduction using FMA3 FFT length 192 on 2^3775-7
Calling N-1 BLS with factored part 100.00% and helper 0.32% (300.40% proof)


2^3775-7 is prime! (0.0393s+0.0008s)
[Elapsed time: 5.00 seconds]


Helper File:
2
3
5
47
83
277
1013
1657
9431
10169
13367
30269
39607
178481
181549
2796203
12112549
21698431
43249589
62209711
164511353
8831418697
112410858169
1484493554507
36368413831997333
138325941036565103
28554501136089979495033
2784254414828346243382561
9280993516297855054039457
57644473457648767005697802783
1112321273705537423158810077602360080577
18216825757346323511608206491538778004307592723
234355755109811973087400958676098128093617121853664147218053
14077694954404816541342489070032607...(146 digits)...21285635126141646218102390822115051
10801753261773691513340658468468201...(171 digits)...49759454300640753645387500306111631
30870181361961013898760159072707015...(182 digits)...37152656208789869114457597675379297
98638404116561632847613590297128199...(237 digits)...62125580615401251462612688402399013
2399
modified2026-01-28 14:09:32
created2026-01-28 14:09:27
id187594

fieldvalue
prime_id50825
person_id9
machineLinux PII 200
whatprp
notesPFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 19 Running N-1 test using base 23 Running N+1 test using discriminant 37, base 12+sqrt(37) Primality testing 2^3775-7 [N-1/N+1, Brillhart-Lehmer-Selfridge] Calling N-1 BLS with factored part 4.03% and helper 0.32% (12.48% proof) 2^3775-7 is Fermat and Lucas PRP! (8.760000 seconds)
modified2003-03-25 17:23:04
created2003-01-04 05:54:49
id60901

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