If 4928 is to 74,

and 3556 is to 58,

what is 2142 to?

**Moderators:** playgirl, JUS, rodbox

Each term is the lowest prime factor of one more than the product of the previous terms.

[So 2*3*7*43+1 = 1807 = 13*139 (both primes) and hence 13 is the fifth term in the sequence.]

So the seventh term in the sequence is obtained by considering 2*3*7*43*13*53+1 = 1244335 = 5*248867 (both primes). Hence the seventh term is 5.

And the next term in the sequence is obtained by considering 2*3*7*43*13*53*5+1 = 6221671 which is prime and is hence the eighth term.

It is conjectured that if you keep repeating this process then eventually all the prime numbers would feature in the sequence (if you can have 'all' of an infinite number of primes). But of course the numbers involved in the multiplications would be rather large.

If one team wins all three matches while the matches between the other three teams all end in draws then the group winner has nine points and each of the other three teams has two points. And one of those teams would qualify. But you can't qualify with one point so two is the minimum.