An Analysis of the Congruence 1 mod 24 as a Generator of Prime Numbers Greater or Equal to 5

Ferreira, José William Porras; Guardo, Willian

doi:10.9734/bjast/2016/24367

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2022

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“…Now, as it was earlier proven by Porras Ferreira and Willian De Jesus [35] that if m is a composite of primes greater or equal to 5, then m 2 ≡ 1 (mod6).…”

Section: The Main Resultsmentioning

confidence: 68%

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A Simple Algorithm for Prime Factorization and Primality Testing

Hamiss

2022

Journal of Mathematics

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We propose a new simple and faster algorithm to factor numbers based on the nature of the prime numbers contained in such composite numbers. It is well known that every composite number has a unique representation as a product of prime numbers. In this study, we focus mainly on composite numbers that contain a product of prime numbers that are greater than or equal to 5 which are of the form 6 k + 1 or 6 k + 5 . Therefore, we use the condition that every prime or composite P of primes greater than or equal to 5 satisfies P 2 ≡ 1 mod 24 . This algorithm is very fast especially when the difference in the prime components of a composite number (prime gap) is not so large. When the difference between the factors (prime gap) is not so large, it often requires just a single iteration to obtain the factors.

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“…Now, as it was earlier proven by Porras Ferreira and Willian De Jesus [35] that if m is a composite of primes greater or equal to 5, then m 2 ≡ 1 (mod6).…”

Section: The Main Resultsmentioning

confidence: 68%

“…Let p and q be prime numbers greater than or equal to 5. Porras Ferreira and Willian De Jesus [35] proved that prime numbers p and q are representatives of 5 (mod6) or 1 (mod6) implying p ≡ 5 (mod6),…”

Section: The Main Resultsmentioning

confidence: 99%

A Simple Algorithm for Prime Factorization and Primality Testing

Hamiss

2022

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

An Analysis of the Congruence 1 mod 24 as a Generator of Prime Numbers Greater or Equal to 5

Cited by 1 publication

References 0 publications

A Simple Algorithm for Prime Factorization and Primality Testing

A Simple Algorithm for Prime Factorization and Primality Testing

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