This number is a composite.
A prime quadruple is four consecutive primes, such that the first and last differ by 8.
- 1 + 23 * 45678 is prime. [Kulsha]
The rightmost nonzero digit in 4013! (4013 is prime!) is 8. [Ottens]
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]
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 π(n). [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]
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]
Eight eights raised to the eighth power plus one is prime. I.e., 88888888^8 + 1 is prime. [Opao]
(8^8+88888)/8 is prime. Note that eight 8s are used. [Firoozbakht]
(π(0)! + π(1)! + ... + π(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]
For n > 8, prime(n) > π(n) + sigma(n), so 8 is the only number n such that prime(n) = π(n) + sigma(n). [Firoozbakht]
The number of autobiographical primes is composite, but the number of autobiographical composites is prime. [Capelle]
The only known n such that the number of nonalternating knots with n crossings is prime. When n=8, there are 3 such knots. [Post]
The Riemann Hypothesis was number 8 on the list of problems that David Hilbert believed should set the course for the mathematical explorers of the twentieth century.
The only known cube that is the sum of the first n odd primes (3+5=8). [Bajpai]
The digit 8 has yet to make an appearance in the constant 0.269606351971674 ... .
The smallest prime raised to the third power ('TWO CUBED') has eight letters. [Homewood]
The digital root of product of twin primes, except (3, 5). [Gupta]
The sum of the first 8 composite numbers and the sum of the first 8 prime numbers differ only by 1. Does the sum of the first n composite numbers ever divide the sum of the first n primes? [Honaker]
The smallest cube k such that 3^k + k and 3^k - k both are prime. [Bajpai]
8 = 2^3 is the only possible cube "centered and sandwiched" in the middle of two pairs of twins (3,5) and (11,13). That is to say 2^3=8=(3+13)/2=(5+11)/2. [Rivera]