Every odd perfect number has at least 8 distinct prime factors. [Hagis]
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 (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]
((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]
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]
(There are 19 curios for this number that have not yet been approved by an editor.)