The Newman-Shanks-Williams prime reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Newman-Shanks-Williams prime

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, ... (sequence A088165 in OEIS), corresponding to the indices 3, 5, 7, 19, 29, ... (sequence A005850 in OEIS).

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

.

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

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