Proth number

Proth number

English

Etymology

After French mathematician François Proth (1852-1879).

Noun

Proth number (plural Proth numbers)

1. (number theory) Any number of the form k·2ⁿ + 1, where k is odd, n is a positive integer, and 2ⁿ > k.
   • 2006, B. Grégoire, L. Théry, B. Werner, A Computational Approach to Pocklington Certificates, Masami Hagiya, Philip Wadler (editors), Functional and Logic Programming: 8th International Symposium, Proceedings, Springer, LNCS 3945, page 109,

     To generate Pocklington certificates for Proth number^[sic] we add a new entry to the oracle: pocklington -proth k p.

   • 2016, Abhijit Das, Computational Number Theory, Taylor & Francis (CRC Press / Chapman & Hall), page 295,

     Suppose that a Proth number ${\\displaystyle n=k2^{r}+1}$ satisfies the condition that ${\\displaystyle a^{(n-1)/2}\\equiv -1{\\pmod {n}}}$ for some integer ${\\displaystyle a}$. Prove that ${\\displaystyle n}$ is prime.

   • 2014, Adam Spencer, Adam Spencer's Big Book of Numbers, Brio Books, page 388,

     If a Proth number is prime, we call it a Proth prime.

Hyponyms

• Cullen number
• Proth prime

Translations

number of the form k×2^n + 1

Italian: numero di Proth m

See also

• Sierpinski number

Further reading

• Sequence A080075 on the On-Line Encyclopedia of Integer Sequences