Claims

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1969_12_01_grimm: Grimm proves that n+1, ..., n+g have distinct prime divisors p_i dividing n+i for g = [log n/(2 log log n)] and all large n, settling the question for every composite run of that length; refereed in 1969.

1975_03_01_ramachandra_shorey_tijdeman: Ramachandra, Shorey and Tijdeman prove that n+1, ..., n+g have distinct prime divisors p_i dividing n+i for g = [a_3 (log n/log log n)^3] and all n at least 3, settling every composite run of that length; refereed in 1975.

2006_06_01_laishram_shorey: Laishram and Shorey prove that the distinct primes exist for every run of composites n+1, ..., n+k with n at most 19236701629 and any k, by a reduction to the prime gaps and a computation; refereed in 2006.

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