What are Prime Numbers?
A prime number is an integer greater than 1 whose only divisors are 1 and itself. Every integer greater than 1 is either prime or a unique product of primes. This is the Fundamental Theorem of Arithmetic: every number has exactly one prime factorisation.
Euclid proved around 300 BC that there are infinitely many primes. Suppose there were a largest prime p. Multiply all known primes together and add 1. The result is either prime itself (contradiction) or has a prime factor not in your list (contradiction). The primes never end.
| Prime | # | Prime | # | Prime | # |
|---|---|---|---|---|---|
| 2 | 1 | 19 | 8 | 37 | 12 |
| 3 | 2 | 23 | 9 | 41 | 13 |
| 5 | 3 | 29 | 10 | 43 | 14 |
| 7 | 4 | 31 | 11 | 47 | 15 |
| 11 | 5 | 37 | 12 | 53 | 16 |
| 13 | 6 | 41 | 13 | 59 | 17 |
| 17 | 7 | 43 | 14 | 61 | 18 |
PlayMemorize uses the primes from 2 to 7919 (the first 1000 primes). The prime number theorem tells us the nth prime is approximately n·ln(n). Prime 1000 is 7919, close to the estimate 1000·ln(1000) ≈ 6908. The distribution of prime gaps is governed by the Riemann Hypothesis.
Every even integer greater than 2 is the sum of two primes. For example: 4 = 2 + 2, 6 = 3 + 3, 100 = 3 + 97. Proposed by Christian Goldbach in a letter to Euler in 1742 and verified for every even number up to 4 x 10^18, it remains unproved. It is one of the oldest unsolved problems in mathematics.
A prime number is a positive integer greater than 1 whose only divisors are 1 and itself. Euclid proved there are infinitely many primes around 300 BC. The Fundamental Theorem of Arithmetic states every integer greater than 1 has a unique prime factorisation. The prime number theorem says the nth prime is approximately n*ln(n). PlayMemorize trains the first 1000 primes (from 2 to 7919). Whether every even number is the sum of two primes (Goldbach's conjecture) remains unproved after 280 years.
Pi
Memorize pi, e, and 38 mathematical constants using the numpad path method
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