Difference between revisions 62813862 and 63105338 on enwiki

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. However, one need not stop there; ⏎
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== Every natural number ≥ 2 has related symmetric primes ==⏎
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[[Goldbach's conjecture]], for example, implies that there are an infinite number of symmetric primes (not necessarilyis at least one (pair of, not necessarily distinct) symmetric primes for every [[natural number]] ''n'' ≥ 2. Assuming then that symmetric primes may have distianct) — in fact, one or more 0 (ie ''p'' = ''q'' = ''n''), this conjecture might be for  mall ''n'' ≥ 2. (y expressed as:

:Let ''n'' be a [[natural number]] ≥ 2 and ''p'',''q'' primes. If ''p'' + ''q'' = 2''n'', then ''p'',''q'' are symmetric primes over ''n''.)⏎
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Clearly the lower bound of ''n'' should be increased if one were to insist that symmetric primes be distinct, ie have a minimal distance of 1 (''q'' - ''n'' = ''n'' - ''p'' = 1), but we shall not make this a matter of interest here. Nevertheless, it is always helpful to regard 2 and 3 as special cases in the study of primes since all other primes are either of the form 6''k'' - 1 or 6''k'' + 1, respectively ''p'' ≡ 5 (mod 6) and ''p'' ≡ 1 (mod 6).

==See also==
* [[Prime number]]
* [[Twin primes]]
* [[Cousin prime]]
* [[Sexy prime]]

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[[Category:Prime numbers]]
[[fr:Nombre premier d'Euler]]
[[zh:欧拉素数]]