9^8 + 8^7 + 7^6 + 6^5 + 5^4 + 4^3 + 3^2 + 2^1 + 1^0 is prime. [Silva]
All digits of the prime 2 * 103020 - 1 are 9 except 1. It contains 3021 digits. [Williams]
9 is the smallest "April Fool prime."
For every prime p with p not equal to 2 and p not equal to 5, there is some number with all digits equal to 9 such that p divides evenly into this number.
There are no consecutive-digit primes starting with 9 with digits in descending order. [Madachy]
Define a certain number of irregularly marked points, n, along the rim of a paper circle, then cut along straight lines that join all possible pairs of points. If n = 9, a prime number of separate pieces will be created. 163 to be exact!
The smallest odd Giuga number must have at least 9 prime factors.
Washington University in St. Louis provides a page that calculates the prime factors of a number (with a maximum of 9 digits).
There are at least 9 prime numbers between x3 and (x + 1)3 for x greater than or equal to , assuming the Riemann Hypothesis is true.
109 + 9 is prime. [Gupta]
Two raised to the 9th power plus and minus 9 are primes! [Hoefakker]
The first digit to appear as an end-digit in two consecutive primes (139 and 149). [Silva]
19, 109, 1009 and 10009 are primes. No other digit can replace the 9 and yield four primes. [Friend]
The number of known positive integers which are the sum of two primes in exactly two ways is a prime square. [Capelle]
2^^n-9 = 2^(2^(2^(....(2^2)...)))-9 is (for large enough n) always divisible by both 7 and 11. Note that 9 is midway between 7 and 11. [Hartley]
There are exactly 3=(sqrt(9)) pandigital improper fractions that reduce to 9 (provided each digit is used once). [Patterson]
9 is the only number m such that m = ((m)!). [Firoozbakht]
The only non-prime digit that is the difference of consecutive squares. [Silva]
The smallest composite number n such that both 2n+n and 2n-n are prime. That is, 29+9 = 521 and 29-9 = 503 are prime. [Poo Sung]
9+8^7+6^5+4^3+2^1 is prime. [Silva]
The only known integer n, such that 2^n-n^2 and 2^n+n^2 are both primes, i.e., 431 and 593. [Loungrides]
Regular nonagon is the only regular polygon such that n^n +(n-2)*180/n (387420629) and ((n-2)*180/n)^n+n (20661046784000000009) are both prime. Note that (n-2)*180/n is an internal angel of a regular polygon. [Sariyar]
(There are 12 curios for this number that have not yet been approved by an editor.)