10 = 2 + 3 + 5 (sum of the first 3 primes).
The smallest unresolved non-prime order to Lam's Problem.
11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99 + 1010 is prime. [Kulsha]
There exists a polynomial in 10 variables with integer coefficients such that the set of primes equals the set of positive values of this polynomial obtained as the variables run through all nonnegative integers. [Ribenboim]
If the number of the month and the number of the day are relatively prime, then June has the fewest such days ... 10.
10! - 9! + 8! - 7! + 6! - 5! + 4! - 3! + 2! - 1! is prime. [Poo Sung]
The Top 10 is a catalogue of primal configurations by Rudolf Ondrejka.
The smallest even number whose square is the sum of n first primes. [Gallardo]
10! = 3! 5! 7! Note the first three consecutive odd primes. [Capelle]
10 ones plus 10 is prime. This is the smallest such two-digit number. [Opao]
10! + 11 and 10! - 11 are primes. [Patterson]
10!+9!+8!+ ... +2!+1!+0!+1!+2!+ ... +8!+9!+10! is prime. [Silva]
10 is the only number n such that n^2 = prime(2*n) + prime(n). [Firoozbakht]
The largest number N such that any set of N consecutive integers contains at least one integer relatively prime to all other integers in the set. [Rupinski]
(10) = prime(1!) + prime(0!) [Firoozbakht]
In the year '10 of this (or any) century, a person born in '73 of the previous century will be 37 and a person born in '37 will be 73. This pattern is true of many different years and ages, but this is the only pattern represented by two emirps. [Green]
The number of known perfect powers n with no primes between n and the next larger perfect power. [Capelle]
10+98765432123456789+10 is prime. [Silva]
10^10+9^10+8^10+7^10+6^10+5^10+4^10+3^10+2^10+1^10+2^10+3^10+4^10+5^10+6^10+7^10+8^10+9^10+10^10 is an 11-digit prime. [Silva]
10 question quiz on prime numbers.
The only even number which can be expressed as the sum of three consecutive primes. [Silva]
10 is the only 1 semiprime with end-digit 0. [Silva]
The 10 prime numbers 1103, 1109, 1117, 1667, 1877, 3001, 3389, 3559, 4001, and 4517 each has the same Collatz trajectory length as its prime index. There are no more of these in the first billion primes. Are there any more at all? [Gaydos]
(There are 25 curios for this number that have not yet been approved by an editor.)