71 (number)
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | seventy-one | |||
| Ordinal | 71st (seventy-first) | |||
| Factorization | prime | |||
| Prime | 20th | |||
| Divisors | 1, 71 | |||
| Greek numeral | ΟΑ´ | |||
| Roman numeral | LXXI | |||
| Binary | 10001112 | |||
| Ternary | 21223 | |||
| Quaternary | 10134 | |||
| Quinary | 2415 | |||
| Senary | 1556 | |||
| Octal | 1078 | |||
| Duodecimal | 5B12 | |||
| Hexadecimal | 4716 | |||
| Vigesimal | 3B20 | |||
| Base 36 | 1Z36 | |||
71 (seventy-one) is the natural number following 70 and preceding 72.
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 [math]\displaystyle{ 9!+1 }[/math] 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 [math]\displaystyle{ 71^{2}=7!+1 }[/math].[6]
It is centered heptagonal number.[7]
See also
- 71 (disambiguation)
References
- ↑ Sloane, N. J. A., ed. "Sequence A006567 (Emirps (primes whose reversal is a different prime))". OEIS Foundation. https://oeis.org/A006567.
- ↑ "Mathematical spandrels". Australasian Journal of Philosophy 95 (4): 779–793. January 2017. doi:10.1080/00048402.2016.1262881.
- ↑ Sloane, N. J. A., ed. "Sequence A002267 (The 15 supersingular primes)". OEIS Foundation. https://oeis.org/A002267.
- ↑ Duncan, John F. R. (2016). "The Jack Daniels problem". Journal of Number Theory 161: 230–239. doi:10.1016/j.jnt.2015.06.001.
- ↑ Sloane, N. J. A., ed. "Sequence A063980 (Pillai primes)". OEIS Foundation. https://oeis.org/A063980.
- ↑ Berndt, Bruce C.; Galway, William F. (2000). "On the Brocard–Ramanujan Diophantine equation [math]\displaystyle{ n!+1=m^2 }[/math]". Ramanujan Journal 4 (1): 41–42. doi:10.1023/A:1009873805276.
- ↑ Sloane, N. J. A., ed. "Sequence A069099 (Centered heptagonal numbers)". OEIS Foundation. https://oeis.org/A069099.
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