prime numbers

Hi

Something i've noticed about prime numbers. If you multiply consecutive prime numbers i.e. 2x3x5=30
and then add the other consecutive primes you get a prime or a prime x prime.

30+7= 37
30+11=41
30+13=43
30+17=47
30+19= 49 (7x7)

Phil

Re: prime numbers

17*19 + 23 + 29 = 375 which is 5*5*5*3

Re: prime numbers

I used python to test this out and it quickly became unwieldy, although I managed to get some results.

Multiplying consecutive primes starting from 2 and adding the last consecutive prime.

Code:

6 + 5 = 11 is prime 30 + 7 = 37 is prime 210 + 11 = 221 13 * 17 2310 + 13 = 2323 23 * 101 30030 + 17 = 30047 is prime 510510 + 19 = 510529 is prime 9699690 + 23 = 9699713 is prime 223092870 + 29 = 223092899 127 * 1231 * 1427 False 6469693230 + 31 = 6469693261 107 * 787 * 76829 False

Multiplying consecutive primes and then adding any greater prime.

Code:

2x3 = 6 6 + 5 = 11 -> is prime 6 + 7 = 13 -> is prime 6 + 11 = 17 -> is prime 6 + 13 = 19 -> is prime 6 + 17 = 23 -> is prime 2x3x5 = 30 30 + 7 = 37 -> is prime 30 + 11 = 41 -> is prime 30 + 13 = 43 -> is prime 30 + 17 = 47 -> is prime 30 + 19 = 49 -> 7 * 7 2x3x5x7 = 210 210 + 11 = 221 -> 13 * 17 210 + 13 = 223 -> is prime 210 + 17 = 227 -> is prime 210 + 19 = 229 -> is prime 210 + 23 = 233 -> is prime 2x3x5x7x11 = 2310 2310 + 13 = 2323 -> 23 * 101 2310 + 17 = 2327 -> 13 * 179 2310 + 19 = 2329 -> 17 * 137 2310 + 23 = 2333 -> is prime 2310 + 29 = 2339 -> is prime 2x3x5x7x11x13 = 30030 30030 + 17 = 30047 -> is prime 30030 + 19 = 30049 -> 151 * 199 30030 + 23 = 30053 -> 41 * 733 30030 + 29 = 30059 -> is prime 30030 + 31 = 30061 -> 23 * 1307 2x3x5x7x11x13x17 = 510510 510510 + 19 = 510529 -> is prime 510510 + 23 = 510533 -> 83 * 6151 510510 + 29 = 510539 -> 31 * 43 * 383 False 510510 + 31 = 510541 -> 307 * 1663 510510 + 37 = 510547 -> 139 * 3673 2x3x5x7x11x13x17x19 = 9699690 9699690 + 23 = 9699713 -> is prime 9699690 + 29 = 9699719 -> 47 * 47 * 4391 False 9699690 + 31 = 9699721 -> 23 * 421727 9699690 + 37 = 9699727 -> is prime 9699690 + 41 = 9699731 -> is prime 2x3x5x7x11x13x17x19x23 = 223092870 223092870 + 29 = 223092899 -> 127 * 1231 * 1427 False 223092870 + 31 = 223092901 -> 43 * 5188207 223092870 + 37 = 223092907 -> is prime 223092870 + 41 = 223092911 -> 29 * 29 * 265271 False 223092870 + 43 = 223092913 -> 6971 * 32003

I thought I might as well post it.

Could only find 6 occurrences where this was False. This is a small sample, but I think you were on to something, at least for a quick way of finding a number which is likely prime or semi-prime.