Interesting line of inferring... I am quite aware how dense primes are, but that might not be enough.
I have counted all these 4x4 (decimal) crossprimes. There are 913,425,530 of them if leading zeros are allowed. But only 406,721,511 without leading zeros.
if leading zeros ARE allowed, then there are certainly arbitrary large crossprimes out there. But if leading zeros aren't allowed, I am not that sure. I have no proof, of course.
If it's worth saying, but not worth its own post, then it goes here.
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