number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

, sexy primes are

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s that differ from each other by . For example, the numbers and are a pair of sexy primes, because both are prime and

11 - 5 = 6

. The term "sexy prime" is a

pun A pun, also known as a paronomasia in the context of linguistics, is a form of word play that exploits multiple meanings of a term, or of similar-sounding words, for an intended humorous or rhetorical effect. These ambiguities can arise from t ...

stemming from the

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

word for six: . If or (where is the lower prime) is also prime, then the sexy prime is part of a prime triplet. In August 2014, the

Polymath A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, ...

group, seeking the proof of the twin prime conjecture, showed that if the generalized Elliott–Halberstam conjecture is proven, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 6 and as such they are either

twin Twins are two offspring produced by the same pregnancy.MedicineNet > Definition of Twin Last Editorial Review: 19 June 2000 Twins can be either ''monozygotic'' ('identical'), meaning that they develop from one zygote, which splits and forms two ...

cousin A cousin is a relative who is the child of a parent's sibling; this is more specifically referred to as a first cousin. A parent of a first cousin is an aunt or uncle. More generally, in the kinship system used in the English-speaking world, ...

or sexy primes. The sexy primes (sequences and in OEIS) below 500 are: :(5,11), (7,13), (11,17), (13,19), (17,23), (23,29), (31,37), (37,43), (41,47), (47,53), (53,59), (61,67), (67,73), (73,79), (83,89), (97,103), (101,107), (103,109), (107,113), (131,137), (151,157), (157,163), (167,173), (173,179), (191,197), (193,199), (223,229), (227,233), (233,239), (251,257), (257,263), (263,269), (271,277), (277,283), (307,313), (311,317), (331,337), (347,353), (353,359), (367,373), (373,379), (383,389), (433,439), (443,449), (457,463), (461,467).

References

External links

* * {{Prime number classes Classes of prime numbers Unsolved problems in number theory