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Euler prime
In [[number theory]], '''Euler primes''' or '''symmetric primes''' are [[prime number|prime]]s that are the same distance from a given integer. For example 3 and 13 are both 5 units from the number 8, hence are symmetric primes. All [[twin prime]]s, [[cousin prime]]s, and [[sexy prime]]s are symmetric primes.

Euler/symmetric primes constitute a ''Goldbach partition'', which is defined as a pair of primes ''p'',''q'' that sum to an even integer. It would appear that all three terms are synonymous, the latter one seemingly most used in the literature.⏎
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== Every natural number &ge; 2 has related symmetric primes ==

[[Goldbach's conjecture]] implies that there is at least one (pair of, not necessarily distinct) symmetric primes for every [[natural number]] ''n'' &ge; 2. Assuming then that symmetric primes ''p'',''q'' may have distance 0 (ie, ''p'' = ''q'' = ''n''), this conjecture might be formally expressed as:

(contracted; show full)* [[Twin primes]]
* [[Cousin prime]]
* [[Sexy prime]]

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[[Category:Prime numbers]]
[[fr:Nombre premier d'Euler]]
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