A 'formula for primes'

Rule

Each term is: The number multiplied by the next larger number plus forty-one

Known as: A 'formula for primes'

The formula found by Euler who noted that the function

n^2 + n + 41

gives prime numbers for all the values of n from n=0 to n=39.

It fails at n=40 which gives 41^2, obviously not a prime.

The first 50 terms (starting from n=0) are:

41 43 47 53 61 71 83 97 113 131 151 173 197 223 251 281 313 347 383 421 461 503 547 593 641 691 743 797 853 911 971 1033 1097 1163 1231 1301 1373 1447 1523 1601 1681 1763 1847 1933 2021 2111 2203 2297 2393 2491

Example

To get the value for n=12:

• Multiply by the next larger number (13), giving 156.
• Add forty-one, giving 197.

So the result is 197.