| This prime number can be unpacked into the original source code for DeCSS, the software that decodes the DVD encryption scheme. |
| The fact that periodical cicadas emerge after a prime number of years could be just a coincidence. |
| More generally, Mersenne primes fit the pattern 2p –1, where p is any prime number. |
| According to the prime number theorem, the average gap length up to a certain prime equals the value of the natural logarithm of that prime. |
| Such a sequence consists of the remainders, or residues, after squaring consecutive whole numbers, then dividing them by a given prime number. |
| The following year he published An elementary proof of the prime number theorem for arithmetic progressions. |
