← 70 71 72 →
Cardinalseventy-one
Ordinal71st
(seventy-first)
Factorizationprime
Prime20th
Divisors1, 71
Greek numeralΟΑ´
Roman numeralLXXI
Binary10001112
Ternary21223
Senary1556
Octal1078
Duodecimal5B12

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

## In mathematics

71 is:

• the 20th prime number. The next is 73, with which it composes a twin prime.
• a permutable prime and emirp with 17.
• the largest number which occurs as a prime factor of an order of a sporadic simple group.
• the sum of three consecutive primes: 19, 23, and 29.
• a centered heptagonal number.[1]
• an Eisenstein prime with no imaginary part and real part of the form ${\displaystyle 3n-1}$.
• a Pillai prime, since ${\displaystyle 9!+1}$ is divisible by 71, but 71 is not one more than a multiple of 9.[2]
• the largest (15th) supersingular prime, which is also a Chen prime.[3]
• part of the last known pair (71, 7) of Brown numbers, since ${\displaystyle 71^{2}=7!+1}$.
• the twenty-third term of the Euclid–Mullin sequence, as it is the least prime factor of one more than the product of the first twenty-two terms.[4]
• the smallest positive integer d such that the imaginary quadratic field ${\displaystyle {\text{Q)){\sqrt {-d))}$ has class number = 7.[5]
• the algebraic degree of Conway's constant, a remarkable number arising in the study of look-and-say sequences.
• the sum of primes less than 71 (2 through 67) is 568, which is divisible by 71.
• 71 is the only number between 1 and 100 that is one less or one more than divisible by all numbers from 2 to 10 (70: 2, 5, 7, 10) (72: 2, 3, 4, 6, 8, 9).
• 71 is an index of a prime Lucas number. [6]

## In other fields

 See also: List of highways numbered 71

Seventy-one is also:

## References

1. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
2. ^ "Sloane's A063980 : Pillai primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
3. ^ "Sloane's A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
4. ^ "Sloane's A000945 : Euclid-Mullin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
5. ^ "Tables of imaginary quadratic fields with small class number". numbertheory.org.
6. ^ "Indices of prime Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-10-10.