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8 times the 8^th prime has a digit sum of 8.

A prime quadruple is four consecutive primes, such that the first and last differ by 8.

- 1 + 2³ x 45678 is prime. [Kulsha]

The smallest number which is the sum of two distinct odd primes.

The rightmost nonzero digit in 4013! (4013 is prime!) is 8. [Ottens]

The smallest cube which is the sum of a twin prime pair {3 + 5}. [Trotter]

The smallest number which is both a sum of prime squares and a prime cube (8 = 2² + 2² = 2³). [Kulsha]

The absolute difference between two odd prime squares is always a multiple of 8. [Capelle]

A Gaussian prime is a Gaussian integer p with exactly 8 divisors. [Smith]

Left-truncatable primes p of length n with the additional property that no prime with length n + 1 can have its leftmost digit removed to produce p are called Henry VIII primes.

8 ones plus 8 is prime. [Opao]

8 is the smallest sum of two factorials of distinct primes (2! + 3!). [Gevisier]

The largest number in which n is exactly twice (n). [Murthy]

Let p and q be odd primes. If p divides 2^q - 1, then p 1 (mod q) and p + 1 (mod 8).

The largest composite number such that all its proper divisors + 1 are primes. [Murthy]

(10⁸ - 8)/8 is prime. [Luhn]

(10⁸⁺⁸ - 8)/8 is also prime. Thanks Mr. Luhn! [Poo Sung]

The first 'not possible' occurrence of summing k consecutive primes such that the total is prime happens when k = 8. [De Geest]

No Fibonacci number greater than 8 is ever of the form p-1 or p+1 where p is a prime number. [Honsberger]

The smallest composite Fibonacci number. [Gupta]

The 8th Fibonacci number plus and minus 8 is prime, i.e., F(8)-8 and F(8)+8 are primes. It is the smallest Fibonacci number to have this property. [Opao]

The product of the first k nonzero Fibonacci numbers + 1 is prime for k = 1, 2, 3, 4, 5, 6, 7, and 8.

Eight eights raised to the eighth power plus one is prime. I.e., 88888888^8 + 1 is prime. [Opao]

The first difference between consecutive primes of 8 is after 8*11+1. This is the last maximal gap of 4 consecutive even numbers. [Nicholson]

(8^8+88888)/8 is prime. Note that eight 8s are used. [Firoozbakht]

((0)! + (1)! + ... + (k)!) is prime only for k = 1,2,..,8 (composite for k>8). [Firoozbakht]

8 is the smallest composite number which can be represented as sum of two primes (i.e., 3 + 5) as well as sum of two composite numbers (i.e., 4 + 4). [Capelle]

8 is the only single-digit cube of a prime. [Silva]

Let R(n) = (10ⁿ - 1)/9 and T_n = the nth triangular number. The first 8 numbers generated by the formula T_R(n) + 1 are prime. [Wesolowski]