1227750359 · 23780 + 5
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: | 1227750359 · 23780 + 5 |
|---|---|
| Verification status (*): | Proven |
| Official Comment (*): | Consecutive primes arithmetic progression (3,d=6), ECPP |
| Proof-code(s): (*): | c14 : Fougeron, Primo |
| Decimal Digits: | 1147 (log10 is 1146.9824936796) |
| Rank (*): | 124196 (digit rank is 3) |
| Entrance Rank (*): | 40324 |
| Currently on list? (*): | no |
| Submitted: | 8/23/2000 12:51:48 UTC |
| Last modified: | 2/4/2026 10:40:04 UTC |
| Database id: | 49914 |
| Status Flags: | none |
| Score (*): | 25.7009 (normalized score 0) |
Archival tags:
There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.
- Arithmetic Progressions of Primes (archivable class *)
- Prime on list: no, rank 182, weight 30.194627918477
Subcategory: "3/3"
(archival tag id 235335, tag last modified 2025-02-16 14:52:00)- Consecutive Primes in Arithmetic Progression (archivable class *)
- Prime on list: no, rank 50
Subcategory: "3/3"
(archival tag id 238814, tag last modified 2025-02-16 14:52:00)- Elliptic Curve Primality Proof (archivable *)
- Prime on list: no, rank 1117
Subcategory: "ECPP"
(archival tag id 185238, tag last modified 2026-01-31 06:37:12)
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.
field value prime_id 49914 person_id 9 machine Using: Digital Ocean Droplet what prime notes Command: /var/www/clientpool/1/pfgw64 -V -f -tc -hhelper_1100000007613269050.txt -q"1227750359*2^3780+5" >command_output 2>&1
PFGW Version 4.0.4.64BIT.20221214.x86_Dev [GWNUM 30.11]
Primality testing 1227750359*2^3780+5 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Reading factors from helper file helper_1100000007613269050.txt
trial
Running N-1 test using base 2
Special modular reduction using zero-padded FMA3 FFT length 384 on 1227750359*2^3780+5
Running N+1 test using discriminant 23, base 1+sqrt(23)
Special modular reduction using zero-padded FMA3 FFT length 384 on 1227750359*2^3780+5
Running N+1 test using discriminant 23, base 3+sqrt(23)
Special modular reduction using zero-padded FMA3 FFT length 384 on 1227750359*2^3780+5
Calling N+1 BLS with factored part 100.00% and helper 0.18% (300.21% proof)
1227750359*2^3780+5 is prime! (0.0626s+0.0001s)
[Elapsed time: 5.00 seconds]
Helper File:
2
3
7
5
17
1483
22051
554977
4086431
1339973561
56853857081142518675946269335556169...(1116 digits)...38741252659326187510552827346271697modified 2026-02-04 10:40:04 created 2026-02-04 10:39:59 id 187707
field value prime_id 49914 person_id 9 machine Linux PII 200 what prp notes PFGW Version 20020311.x86_Dev (Alpha software, 'caveat utilitor') Running N-1 test using base 2 Running N+1 test using discriminant 23, base 1+sqrt(23) Primality testing 1227750359*2^3780+5 [N-1/N+1, Brillhart-Lehmer-Selfridge] Calling N+1 BLS with factored part 0.84% and helper 0.18% (2.76% proof) 1227750359*2^3780+5 is Fermat and Lucas PRP! (7.130000 seconds) modified 2003-03-25 17:23:04 created 2003-01-04 05:55:22 id 60908
Query times: 0.0003 seconds to select prime, 0.0003 seconds to seek comments.
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