This can be abbreviated to NSW, which is also the abbreviation of the state of New South Wales in Australia.

In mathematics, a Newman-Shanks-Williams prime (often abbreviated NSW prime) is a certain kind of prime number. A prime p is an NSW prime iff it is a Newman-Shanks-Williams number; that is, if it can be written in the form

NSW primes were first described by M. Newman , D. Shanks and H. C. Williams in 1981 during the study of finite groups with square order.

The first few NSW primes are 7, 41, 239, 9369319, 63018038201, ... , corresponding to the indices 3, 5, 7, 19, 29, ... (sequence A005850 in OEIS).

The sequence S alluded to in the formula can be described by the following recurrence relation:

S₀ = 1

S₁ = 1

.

The first few terms of the sequence are 1, 1, 3, 7, 17, 41, 99, ... (sequence A001333 in OEIS). These numbers also appear in the continued fraction convergents to √2.

External links

• The Prime Glossary: NSW number

Further reading

• M. Newman, D. Shanks and H. C. Williams, Simple groups of square order and an interesting sequence of primes, Acta. Arith., 38:2 (1980/81) 129-140.