Proof-code: p449

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Samuel Yates began, and this site continues, a database of the largest known primes. Primes in that database are assigned a proof-code to show who should be credited with the discovery as well as what programs and projects they used. (Discoverers have one prover-entry, but may have many proof-codes because they use a variety of programs...)

This page provides data on p449, one of those codes.

Code name (*): p449 (See the descriptive data below.)

Persons (*): 1 (counting humans only)

Projects (*): 0 (counting projects only)

Display (HTML): Rodriguez2, OpenPFGW

Number of primes: total 3

Unverified Primes: 0 (prime table entries marked 'Composite','Untested', or 'InProcess'

Score for Primes (*): total 46.9259, on current list 46.9259 (normalized score 4)

Entrance Rank (*): mean 38854.00 (minimum 976, maximum 57793)

Descriptive Data: (report abuse)

These primes follow the format n = p * q + 1 or n = p * q - 1.
The prime p has already been proven prime (in these cases, a Mersenne prime is used).
To prove primality using PFGW, a Pocklington or Morrison test is performed with a helper file.
This method applies Pocklington’s theorem and a theorem by Morrison, adapted for finding primes. More details can be found in the TechRxiv publication.
For sieving, I used SGSA (Stage GCD Sieving Algorithm), a novel and efficient method that effectively replaces trial division and ECM in this context. The script and documentation are available at the GitHub repository.

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Below is additional information about this entry.

Display (text): Rodriguez2, OpenPFGW

Display (short): Rodriguez2

Database id: 10307 (do not use this database id, it is subject to change)

Proof program: PrimeForm The primes from this code accounts for 0.527% of the (active) primes and 0.253% of the (active) score for this program.

Entry last modified: 2025-09-18 13:37:13

Code name (*):	p449 (See the descriptive data below.)
Persons (*):	1 (counting humans only)
Projects (*):	0 (counting projects only)
Display (HTML):	Rodriguez2, OpenPFGW
Number of primes:	total 3
Unverified Primes:	0 (prime table entries marked 'Composite','Untested', or 'InProcess'
Score for Primes (*):	total 46.9259, on current list 46.9259 (normalized score 4)
Entrance Rank (*):	mean 38854.00 (minimum 976, maximum 57793)

Display (text):	Rodriguez2, OpenPFGW
Display (short):	Rodriguez2
Database id:	10307 (do not use this database id, it is subject to change)
Proof program:	PrimeForm The primes from this code accounts for 0.527% of the (active) primes and 0.253% of the (active) score for this program.
Entry last modified:	2025-09-18 13:37:13