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It is easy to prove that there are an infinite number of primes. If there were a finite number of primes, you could multiply them all together and add 1. The resulting number would show the existence of a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1).
It is easy to prove that there are an infinite number of primes. If there were a finite number of primes, you could multiply them all together and add 1. The resulting number would show the existence of a new prime, since it would not be divisible by any smaller prime (it would always have a remainder of 1).
To construct a table of prime numbers, you would use a method called the '''Sieve of Eratosthenes'''. Simply write down an ordered list of all counting numbers greater than 1. Beginning with 2*2 = 4, cross out every second number:
:2 3 <s>4</s> 5 <s>6</s> 7 <s>8</s> 9 <s>10</s> 11 ...
then beginning with 3*3 = 9 cross out every third number:
:2 3 <s>4</s> 5 <s>6</s> 7 <s>8 9 10</s> 11 ...
Beginning with 5*5 = 25, cross out every fifth number, then repeat for the primes 7, 11, 13, etc. The result will be a table of primes which is accurate up to ''n''-squared, where ''n'' is the largest number you sieved for.