Solinas prime

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In mathematics, a Solinas prime, named after Jerome Solinas, is a prime number of the form 2^a ± 2^b ± 1, where 0 < b < a.

For example, the first five pairs of twin primes are also Solinas primes.

The first few Solinas primes are

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 59, 61, 67, 71, 73, 79, 97, … (sequence A165255 in OEIS).

The first odd prime that is not a Solinas prime is 43.

External links [edit]

Jerome A. Solinas, "Generalized Mersenne Numbers" (pdf)

v t e Prime number classes

By formula	Fermat (2^2ⁿ + 1) Mersenne (2^p − 1) Double Mersenne (2^{2^p−1} − 1) Wagstaff (2^p + 1)/3 Proth (k·2ⁿ + 1) Factorial (n! ± 1) Primorial (p_n# ± 1) Euclid (p_n# + 1) Pythagorean (4n + 1) Pierpont (2^u·3^v + 1) Solinas (2^a ± 2^b ± 1) Cullen (n·2ⁿ + 1) Woodall (n·2ⁿ − 1) Cuban (x³ − y³)/(x − y) Carol (2ⁿ − 1)² − 2 Kynea (2ⁿ + 1)² − 2 Leyland (x^y + y^x) Thabit (3·2ⁿ − 1) Mills (floor(A^3ⁿ))

By integer sequence	Fibonacci Lucas Motzkin Bell Partitions Pell Perrin Newman–Shanks–Williams

By property	Lucky Wall–Sun–Sun Wilson Wieferich Wieferich pair Fortunate Ramanujan Pillai Regular Strong Stern Supersingular (elliptic curve) Supersingular (moonshine theory) Wolstenholme Good Super Higgs Highly cototient Illegal

Base-dependent	Happy Dihedral Palindromic Emirp Repunit (10ⁿ − 1)/9 Permutable Circular Strobogrammatic Minimal Full reptend Unique Primeval Self Smarandache–Wellin

Patterns	Twin (p, p + 2) Triplet (p, p + 2 or p + 4, p + 6) Quadruplet (p, p + 2, p + 6, p + 8) Tuple Cousin (p, p + 4) Sexy (p, p + 6) Chen Sophie Germain (p, 2p + 1) Cunningham chain (p, 2p ± 1, …) Safe (p, (p − 1)/2) Arithmetic progression (p + a·n, n = 0, 1, …) Balanced (consecutive p − n, p, p + n)

By size	Titanic (1,000+ digits) Gigantic (10,000+) Mega (1,000,000+) Largest known

Complex numbers	Eisenstein prime Gaussian prime

Composite numbers	Pseudoprime Almost prime Semiprime Interprime

Related topics	Probable prime Industrial-grade prime Formula for primes Prime gap

List of prime numbers

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Solinas prime

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