71 (number)

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

Look up seventy-one in Wiktionary, the free dictionary.
← 70 71 72 →
Cardinalseventy-one
Ordinal71st
(seventy-first)
Factorizationprime
Prime20th
Divisors1, 71
Greek numeralΟΑ´
Roman numeralLXXI
Binary10001112
Ternary21223
Senary1556
Octal1078
Duodecimal5B12
Hexadecimal4716

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

References
  1. Sloane, N. J. A. (ed.). "Sequence A006567 (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.). "Sequence A002267 (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.). "Sequence A063980 (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.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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