> I wonder if the largest pair list at A002072 should

These values are indeed the largest known

> include some statement that certain values are

> "smallest known" rather than "smallest", as the

> latter assumes the values can be confirmed in

> some rigorous manner.

(there may be larger ones). Doubt is not about

"smallest" but about "for all i>m".

> I do have a new entry for p = 229, having

For p = 229 we have 5.2*sqrt(p)-7.7 = 71,

> found this pair (S, S+1):

>

> S = 15487655655079919751646464

so I expect N about exp(71), which is much

larger than your N about exp(58).

Best regards,

Andrey- This 181-smooth pair popped up in a random search:

S = 90672220863645734556839376

Factors

S = 2^4, 3^3, 11, 23, 29, 31, 37^2, 73, 97,

139^2, 163, 167, 181

S-1 = 5^4, 13^3, 17, 19, 43, 47, 67^2, 101^2,

113^2, 173

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