### Properties of the number 971:

971 is a cyclic number.971 is the 164

^{th}prime.

971 has 5 antidivisors and 970 totatives.

971 has an emirp digit sum 17 in base 10.

Reversing the decimal digits of 971 results in an emirp.

971 = 486

^{2}- 485

^{2}is the difference of 2 nonnegative squares in 1 way.

971 is the difference of 2 positive pentagonal numbers in 1 way.

971 = 1

^{2}+ 3

^{2}+ 31

^{2}is the sum of 3 positive squares.

971

^{2}is the sum of 3 positive squares.

971 is a proper divisor of 239

^{10}- 1.

971 is an emirp in (at least) the following bases: 3, 4, 7, 8, 10, 15, 16, 17, 23, 25, 33, 35, 37, 38, 41, 42, 43, 46, 49, 50, 53, 54, 55, 57, 59, 62, 64, 69, 70, 73, 77, 81, 82, 86, 87, 89, 93, 97, 98, and 100.

971 is palindromic in (at least) the following bases: 19, -14, and -97.

971 in base 7 = 2555 and consists of only the digits '2' and '5'.

971 in base 13 = 599 and consists of only the digits '5' and '9'.

971 in base 15 = 44b and consists of only the digits '4' and 'b'.

971 in base 18 = 2hh and consists of only the digits '2' and 'h'.

971 in base 19 = 2d2 and consists of only the digits '2' and 'd'.

### The number 971 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A000928: Irregular primes: p is regular if and only if the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) are not divisible by p.

A001913: Full reptend primes: primes with primitive root 10.

A005846: Primes of the form n^2 + n + 41.

A006567: Emirps (primes whose reversal is a different prime).

A007500: Primes whose reversal in base 10 is also prime (called "palindromic primes" by D. Wells, although that name usually refers to A002385). Also called reversible primes.

A030430: Primes of the form 10*n+1.

A046132: Larger member p+4 of cousin primes (p, p+4).

A061955: Numbers n such that n divides the (left) concatenation of all numbers <= n written in base 2 (most significant digit on right).

A141111: Primes of the form 4*x^2+x*y-4*y^2 (as well as of the form 4*x^2+9*x*y+y^2).

A235266: Primes whose base 2 representation is also the base 3 representation of a prime.

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