79 (number)

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 and )
• An isolated prime without a twin prime, as 77 and 81 are composite.
• The smallest prime number p for which the real quadratic field Q[] has class number greater than 1 (namely 3).
• A cousin prime with 83.
• An emirp in base 10, because the reverse of 79, 97, is also a prime.
• A Fortunate prime.
• A circular prime.
• A prime number that is also a Gaussian prime (since it is of the form 4n + 3).
• A happy prime.
• A Higgs prime.
• A lucky prime.
• A permutable prime, with ninety-seven.
• A Pillai prime, because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23.
• A regular prime.
• 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, \frac{1}{79}=\sum_{n=1}^\infty{P(n)\times 10^{-(n+1)}}=0.0126582278\dots\ .
• A Leyland number of the second kind and Leyland prime of the second kind, using 2 & 7 (2^7-7^2)

References

References

1. {{Cite OEIS. A007510. Single (or isolated or non-twin) primes: Primes p such that neither p-2 nor p+2 is prime.
2. H. Cohen, ''A Course in Computational Algebraic Number Theory'', GTM 138, Springer Verlag (1993), Appendix B2, p.507. The table lists fields by [[Real quadratic field#Discriminant. discriminant]], which is 4''p'' for '''Q'''[{{sqrt. ''p''] when ''p'' is [[modular arithmetic. congruent]] to 3 modulo 4, as is the case for 79, so the entry appears at discriminant 316.
3. "Sloane's A006567 : Emirps". OEIS Foundation.
4. "Sloane's A046066 : Fortunate primes". OEIS Foundation.
5. [https://oeis.org/A068652 Numbers such that every cyclic permutation is a prime.]
6. "Sloane's A035497 : Happy primes". OEIS Foundation.
7. "Sloane's A007459 : Higgs' primes". OEIS Foundation.
8. "Sloane's A031157 : Numbers that are both lucky and prime". OEIS Foundation.
9. "Sloane's A063980 : Pillai primes". OEIS Foundation.
10. "Sloane's A007703 : Regular primes". OEIS Foundation.
11. {{Cite OEIS. A045575. Leyland numbers of the second kind
12. {{Cite OEIS. A123206. Leyland prime numbers of the second kind