PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: No information on entry rating
Stern prime (Definition)

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.




"Stern prime" is owned by PrimeFan. [ owner history (1) ]
(view preamble | get metadata)

View style:

Log in to rate this entry.
(view current ratings)

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 MSC11N05 (Number theory :: Multiplicative number theory :: Distribution of primes)

Pending Errata and Addenda
None.
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)