71 (number)

Last updated
70 71 72
Cardinal seventy-one
Ordinal 71st
(seventy-first)
Factorization prime
Prime 20th
Divisors 1, 71
Greek numeral ΟΑ´
Roman numeral LXXI
Binary 10001112
Ternary 21223
Senary 1556
Octal 1078
Duodecimal 5B12
Hexadecimal 4716

71 (seventy-one) is the natural number following 70 and preceding 72.

Contents

In mathematics

Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime. [1] [2] It is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime. [3] [4]

It is a Pillai prime, since is divisible by 71, but 71 is not one more than a multiple of 9. [5] It is part of the last known pair (71, 7) of Brown numbers, since . [6]

It is centered heptagonal number. [7]

See also

Related Research Articles

17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.

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

73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

34 (thirty-four) is the natural number following 33 and preceding 35.

31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.

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300 is the natural number following 299 and preceding 301.

400 is the natural number following 399 and preceding 401.

700 is the natural number following 699 and preceding 701.

2000 is a natural number following 1999 and preceding 2001.

115 is the natural number following 114 and preceding 116.

3000 is the natural number following 2999 and preceding 3001. It is the smallest number requiring thirteen letters in English.

4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.

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References

  1. Sloane, N. J. A. (ed.). "SequenceA006567(Emirps (primes whose reversal is a different prime))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. Baker, Alan (January 2017). "Mathematical spandrels". Australasian Journal of Philosophy. 95 (4): 779–793. doi:10.1080/00048402.2016.1262881. S2CID   218623812.
  3. Sloane, N. J. A. (ed.). "SequenceA002267(The 15 supersingular primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. Duncan, John F. R.; Ono, Ken (2016). "The Jack Daniels problem". Journal of Number Theory. 161: 230–239. doi: 10.1016/j.jnt.2015.06.001 . MR   3435726. S2CID   117748466.
  5. Sloane, N. J. A. (ed.). "SequenceA063980(Pillai primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. Berndt, Bruce C.; Galway, William F. (2000). "On the Brocard–Ramanujan Diophantine equation ". Ramanujan Journal. 4 (1): 41–42. doi:10.1023/A:1009873805276. MR   1754629. S2CID   119711158.
  7. Sloane, N. J. A. (ed.). "SequenceA069099(Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.