71 (seventy-one) is the natural number following 70 and preceding 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 | |||
Look up seventy-one in Wiktionary, the free dictionary.
In mathematics
edit71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) are prime numbers, 71 is an emirp and more generally a permutable prime.[1][2]
71 is a centered heptagonal number.[3]
It is a Pillai prime, since is divisible by 71, but 71 is not one more than a multiple of 9.[4] It is part of the last known pair (71, 7) of Brown numbers, since .[5]
71 is the smallest of thirty-one discriminants of imaginary quadratic fields with class number of 7, negated (see also, Heegner numbers).[6]
71 is the largest number which occurs as a prime factor of an order of a sporadic simple group, the largest (15th) supersingular prime.[7][8]
See also
editReferences
edit- ^ Sloane, N. J. A. (ed.). "Sequence A006567 (Emirps (primes whose reversal is a different prime))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Baker, Alan (January 2017). "Mathematical spandrels". Australasian Journal of Philosophy. 95 (4): 779–793. doi:10.1080/00048402.2016.1262881. S2CID 218623812.
- ^ Sloane, N. J. A. (ed.). "Sequence A069099 (Centered heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A063980 (Pillai primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A046004 (Discriminants of imaginary quadratic fields with class number 7 (negated).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-08-03.
- ^ Sloane, N. J. A. (ed.). "Sequence A002267 (The 15 supersingular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.