Puzzle 1281 Find the largest prime such that any block of two adjacent digits in it...

On August 15, 2026, Bernardo Recamán sent the following puzzle:

1. Find the largest prime B such that any block of two adjacent digits in it, is a two-digit number coprime to all other such blocks in it.
2. Do likewise with blocks of three adjacent digits.
3. Redo 1 & 2 if no internal prime-blocks are permitted.

Examples to 1 & 2:

1) 4783531= prime
47= prime
78= 2x3x13
83= prime
35= 5x7
53=prime
31=prime

2) 47835391 = prime
478= 2x239
783=3x3x3x29
835=5x167
353=prime
539=7x7x11
391=17x23

3) 64951
64 = 2^6
49 = 7^2
95 = 5x19
51 = 3x17

4) 998917
998 = 2x499
989 = 23x43
891 = 3^4x11
917 = 7x131

Q. Send your largest pimes for 1, 2, 3 & 4.
____
BTW this is a puzzle alike to Puzzle 253.