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, … (sequence A165255 in OEIS).

[edit] See also

Mersenne prime

[edit] External links

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 · Permutable · 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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