79 (number)
Template:Infobox number 79 (seventy-nine) is the natural number following 78 and preceding 80.
In mathematics
79 is a Fortunate prime,[1] a circular prime,[2] a happy prime,[3] a Higgs prime,[4] a lucky prime, a regular prime,[5][6] a cousin prime with 83, and a sexy prime with 73. Since it is a prime number of the form Template:Nowrap, it is a Gaussian prime. It is a Pillai prime[7] because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23. It is a right-truncatable prime, because when the last digit (9) is removed, the remaining number (7) is still prime. Because 97 is prime, it is an emirp and a permutable prime in base 10.
79 is the smallest prime number p for which the real quadratic field Q[[[:Template:Sqrt]]] has class number greater than 1 (namely 3).[8]
79 is the smallest number that cannot be represented as a sum of fewer than 19 fourth powers.
Similarly to how the decimal expansion of 1/89 gives Fibonacci numbers, 1/79 gives Pell numbers, that is:
79 is a Leyland prime of the second kind.[9] using 2 & 7: 79 = .
References
External links
- ↑ Template:Cite web
- ↑ Numbers such that every cyclic permutation is a prime.
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ H. Cohen, A Course in Computational Algebraic Number Theory, GTM 138, Springer Verlag (1993), Appendix B2, p.507. The table lists fields by discriminant, which is 4p for Q[[[:Template:Sqrt]]] when p is congruent to 3 modulo 4, as is the case for 79, so the entry appears at discriminant 316.
- ↑ Template:Cite OEIS