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Ah well, that'll teach me to run bc without setting the scale (and not turning my brain on enough to realise a multiple is probably even! :-). But how about 2 * 3 * 5 * 7 * 11 * 13 = 30030 and 30031 = 59 * 509. I think that's right. (Famous last words?)
p1*p2*...*pn + 1 isn't necessarily prime (for example n = 4 gives 2 * 3 * 5 * 7 + 1 = 211 = 13 * 16). But if isn't then it must be divisible by prime other than p1, ..., pn so you've still got the contradiction.
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Ah well, that'll teach me to run bc without setting the scale (and not turning my brain on enough to realise a multiple is probably even! :-).
But how about 2 * 3 * 5 * 7 * 11 * 13 = 30030 and 30031 = 59 * 509. I think that's right. (Famous last words?)
p1*p2*...*pn + 1 isn't necessarily prime (for example n = 4 gives 2 * 3 * 5 * 7 + 1 = 211 = 13 * 16). But if isn't then it must be divisible by prime other than p1, ..., pn so you've still got the contradiction.