My approximation:

There are 9*10^4 five digit numbers with no leading zero.

There are 7*8^4 five digit numbers with no leading zero, containing neither 3 nor 7.

So there are 90000-28672 =61328 numbers satisfying condition 1.

Roughly 1/37 of these numbers i.e 1657 are divisible by 37.

I am happy with this number as an engineer's approximation.

When some solver evaluates the exact number we will comment

upon the accuracy of my approximation.

blackjack

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