## Divisibility question; consecutive numbers

Does anyone know the answer to this problem: if you have a set of consecutive prime numbers (2,3,5,7...), what is the greatest amount of consecutive integers that are divisible by at least one of the prime numbers? For 2,3,and 5, I know it is 5 (2 through 6, 24 through 28, 32 through 36...), but for really big primes I can't figure it out.
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 Blog Entries: 8 Recognitions: Gold Member Science Advisor Staff Emeritus Hi kid1! Lets say you have prime {2,3,5,...,p}, then you can set x=2*3*5*...*p. Then $$x+2,x+3,x+4,...,x+p,x+p+1$$ is a sequence of consecutive integers such that one of the primes divides it. So there certainly are p consecutive integers not divisible by p. It's a good question whether p is the largest number of consecutive integers...
 The largest is probably longer, given that it's easy to find one example longer than the last prime. For {2,3,5,7}, the numbers 2 to 10 (9 of them) are divisible by some prime of the list (because 7 and 11 are not twin). P.S.: I googled this, if it helps someone: http://oeis.org/A058989

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