79 (number)

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 73 and 83)
• 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, ${\displaystyle {\frac {1}{79}}=\sum _{n=1}^{\infty }{P(n)\times 10^{-(n+1)}}=0.0126582278\dots \ .}$
• A Leyland number of the second kind^[11] and Leyland prime of the second kind,^[12] using 2 & 7 (${\displaystyle 2^{7}-7^{2}}$)