7: Difference between revisions

Revision as of 21:52, 2 January 2012

This article is about a particular natural number.|View all articles on particular natural numbers

The number 7 is a prime number.

Property or family	Parameter values	First few numbers	Proof of satisfaction/membership/containment
prime number	fourth prime number	2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, [SHOW MORE] 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271 View list on OEIS	divide and check
Mersenne number $M_{n}=2^{n}-1$	$n=3$ , i.e., $M_{3}=2^{3}-1$		plug and check
Mersenne prime (both a prime number and a Mersenne number)	same as for Mersenne number		combine above
safe prime (odd prime such that half of that minus one is also prime)	second safe prime	5, 7, 11, 23, 47, 59, 83, 107, 167, [SHOW MORE] 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903 View list on OEIS	plug and check $(7-1)/2=3$ is prime.

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 | [[satisfies property::Mersenne prime]] (both a [[prime number]] and a [[Mersenne number]]) || same as for Mersenne number || {{#lst:Mersenne prime|list}} || combine above
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+| [[satisfies property::safe prime]] (odd prime such that half of that minus one is also prime) || second safe prime || {{#lst:safe prime|list}} || plug and check <math>(7 - 1)/2 = 3</math> is prime.
 |}