[QUOTE=uau;599581]

No, you can easily construct an irrational number whose decimal representation consists of only 0 and 1.[/QUOTE]

Hah, silly me

Appended is what I have got up to one trillion digits.

[QUOTE=kruoli;599950]Appended is what I have got up to one trillion digits.[/QUOTE]

Seems to be a reasonable sample set. Thank you for that. Sincerely.

[QUOTE=kruoli;599950]Appended is what I have got up to one trillion digits.[/QUOTE]

Amazing work. But...You numbers overlap I notice - see the results for 67 and 73. In my original definition I disallowed overlaps.

This is correct, I overlooked it. I will run it again with this rule in mind.

These are my updated results. The only indices that changed are those of 71, 73 and all primes in the range 53567-57173. The first two are known from the example in the first post of this thread, the other one is because of the digits …53653657… starting at position 429,388,878, which includes both primes 53653 and 53657.

The series includes a couple of large adjacent primes, at the positions shown

889673 and 889687 at position 61984722855
979291 and 979313 at position 68361333199

This contrasts the very long wait for 1184363 - no less than a 161684719 digit wait

1184357 202059128456
1184363 202220813175