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79 (number)

From Wikipedia, the free encyclopedia
78 79 80
Cardinalseventy-nine
Ordinal79th
(seventy-ninth)
Factorizationprime
Prime22nd
Divisors1, 79
Greek numeralΟΘ´
Roman numeralLXXIX, lxxix
Binary10011112
Ternary22213
Senary2116
Octal1178
Duodecimal6712
Hexadecimal4F16
ASCII valueO

79 (seventy-nine) is the natural number following 78 and preceding 80.

In mathematics

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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 4n + 3, 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[p] 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

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  1. "Sloane's A046066 : Fortunate primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  2. Numbers such that every cyclic permutation is a prime.
  3. "Sloane's A035497 : Happy primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  4. "Sloane's A007459 : Higgs' primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  5. "Sloane's A007703 : Regular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  6. "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  7. "Sloane's A063980 : Pillai primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  8. 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.
  9. Sloane, N. J. A. (ed.). "Sequence A123206 (Leyland prime numbers of the second kind)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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