number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. Formulas for calculating primes do exist; however...

encode all primes, or only primes. One possible formula is based on Wilson's theorem and generates the number 2 many times and all other primes exactly once...

infinite number of prime numbers. Subsets of the prime numbers may be generated with various formulas for primes. The first 1000 primes are listed below...

Functions Over Primes without R.H.". arXiv:1002.0442v1 [math.NT]. Dusart, Pierre (January 2018). "Explicit estimates of some functions over primes". Ramanujan...

the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p. The exponents n which give Mersenne primes are 2, 3, 5...

π(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is the natural logarithm of N. This means that for large enough...

previous primes. Also, there is no effective known general manipulation and/or extension of some mathematical expression (even such including later primes) that...

has been conjectured that infinitely many Wilson primes exist, and that the number of Wilson primes in an interval [ x , y ] {\displaystyle [x,y]} is...

(sequence A000979 in the OEIS) Exponents which produce Wagstaff primes or probable primes are: 3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 79, 101, 127, 167...

23497, 24571, 25117, 26227 (sequence A002407 in the OEIS) The formula for a general cuban prime of this kind can be simplified to 3 y 2 + 3 y + 1 {\displaystyle...

the prime numbers is commonly misinterpreted as defining the primorial primes, in the following manner: Assume that the first n consecutive primes including...

factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even). The first 10 factorial primes (for n...

prime pair. Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to...

A Pythagorean prime is a prime number of the form 4 n + 1 {\displaystyle 4n+1} . Pythagorean primes are exactly the odd prime numbers that are the sum...

Woodall primes and Mersenne primes are W2 = M3 = 7, and W512 = M521. Like Cullen numbers, Woodall numbers have many divisibility properties. For example...

categories of prime numbers: Mersenne primes, which have the form 2 k − 1 {\displaystyle 2^{k}-1} , Crandall or pseudo-Mersenne primes, which have the...

between Wieferich primes and various other topics in mathematics have been discovered, including other types of numbers and primes, such as Mersenne and...

Ramanujan primes. Further generalizations of Ramanujan primes have also been discovered; for instance, there is a proof that 2 p i − n > p i  for  i > k...

infinitely many Pierpont primes, but this remains unproven. Unsolved problem in mathematics Are there infinitely many Pierpont primes? More unsolved problems...

If 2k + 1 is prime and k > 0, then k itself must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2023[update]...

19th century. Interest in these primes first arose due to their connection with Fermat's Last Theorem. Wolstenholme primes are also related to other special...

{p-1}{2}}{\frac {q-1}{2}}}.} There are formulas that use floor to express the quadratic character of small numbers mod odd primes p: ( 2 p ) = ( − 1 ) ⌊ p + 1 4...

Günter (6 May 2017). "Generalized Cullen primes". Harvey, Steven (6 May 2017). "List of generalized Cullen primes base 101 to 10000". Cullen, James (December...

and consider the sequence of x values that gives Leyland primes, for example x2 + 2x is prime for x = 3, 9, 15, 21, 33, 2007, 2127, 3759, ... (OEIS: A064539)...

Rather, he said: consider any finite set of primes (he did not assume that it contained only the first n primes, e.g. it could have been {3, 41, 53}) and...

average gap between primes increases as the natural logarithm of these primes, and therefore the ratio of the prime gap to the primes involved decreases...

.. (sequence A051021 in the OEIS). The primes generated by Mills' constant are known as Mills primes; if the Riemann hypothesis is true, the sequence...

n Fermi–Dirac primes, prime powers whose exponent is a power of two. Clearly, 1 < σ 0 ( n ) < n {\displaystyle 1<\sigma _{0}(n)<n} for all n > 2 {\displaystyle...

a given Boolean formula Boolean prime ideal theorem, a theorem which states that ideals in a Boolean algebra can be extended to prime ideals Binary (disambiguation)...

algorithm Table of divisors Prime number, prime power Bonse's inequality Prime factor Table of prime factors Formula for primes Factorization RSA number...