79 (number)
(Redirected from Seventy-nine)
Template:Infobox number 79 (seventy-nine) is the natural number following 78 and preceding 80.
In mathematics
79 is:
- An odd number.
- The smallest number that can not be represented as a sum of fewer than 19 fourth powers.
- The 22nd prime number (between Template:Num and Template:Num)
- An isolated prime without a twin prime, as 77 and 81 are composite.[1]
- The smallest prime number p for which the real quadratic field Q[√p] has class number greater than 1 (namely 3).[2]
- A cousin prime with 83.
- An emirp in base 10, because the reverse of 79, 97, is also a prime.[3]
- A Fortunate prime.[4]
- A circular prime.[5]
- A prime number that is also a Gaussian prime (since it is of the form 4n + 3).
- A happy prime.[6]
- A Higgs prime.[7]
- A lucky prime.[8]
- A permutable prime, with ninety-seven.
- A Pillai prime,[9] because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23.
- A regular prime.[10]
- A right-truncatable prime, because when the last digit (9) is removed, the remaining number (7) is still prime.
- A sexy prime (with 73).
- The n value of the Wagstaff prime 201487636602438195784363.
- Similarly to how the decimal expansion of 1/89 gives Fibonacci numbers, 1/79 gives Pell numbers, that is,
- A Leyland number of the second kind[11] and Leyland prime of the second kind,[12] using 2 & 7 ()
References
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- ↑ 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[√p] when p is congruent to 3 modulo 4, as is the case for 79, so the entry appears at discriminant 316.
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- ↑ Numbers such that every cyclic permutation is a prime.
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