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If for a given prime number $q$ there is no smaller prime $p$ and nonzero integer $b$ such that $q = 2b^2 + p$ , then $q$ is a Stern prime. These primes were first studied by Moritz Abraham Stern, in connection to a lesser known conjecture of Goldbach's. Like other mathematicians of the time, Stern considered 1 to be a prime number. Thus his list
of Stern primes read thus: 2, 17, 137, 227, 977, 1187, 1493. A century later the list has been amended to include 3 (as in A042978 of Sloane's OEIS) but no terms larger than 1493 have been found. The larger of a twin prime is not a Stern prime.
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"Stern prime" is owned by PrimeFan. [ owner history (1) ]
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Cross-references: twin prime, terms, OEIS, conjecture, connection, Moritz Abraham Stern, integer, prime number
There are 3 references to this entry.
This is version 1 of Stern prime, born on 2006-10-11.
Object id is 8446, canonical name is SternPrime.
Accessed 993 times total.
Classification:
| AMS MSC: | 11N05 (Number theory :: Multiplicative number theory :: Distribution of primes) |
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Pending Errata and Addenda
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