**237373** is a 6-digit prime number where all its digits are prime and every pair of consecutive digits is a prime.

Here’s another example, **537373**

It’s a 6-digit prime number that shares the same properties.

**237373737373** is a 12-digit prime number with the same properties.

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The next such prime found has 42 digits:

237373737373737373737373737373737373737373

Nice!

And for another prime number (537373), the next such prime found has 26 digits:

53737373737373737373737373

One more example for (537373) has 44 digits :

53737373737373737373737373737373737373737373

Awesome!

Added one more example for (537373) that has 48 digits :

537373737373737373737373737373737373737373737373

Here are the 6 to 12 digit primes whos digits are prime and each consecutive 3 digits are prime.

{727733}

{5577337}, {5773373}

{55773373}

{257733733}, {773373373}

{2577337337}

{52337337337}

{277337337337}, {577337337337}

Paul.

Another similar set of primes whose digits are prime and every pair of consecutive digits is a prime.

{73373737}, 8-digit

{73373737373737}, 14-digit

{7337373737373737373737373737373737373737373737}, 46-digit

{73373737373737373737373737373737373737373737373737373737373737}, 62-digit. It is the largest prime of this form less than a googol.

The next few are with digit length 140, 292 and 638 and no more up to 2000 digits

P.

{73535353535353535353535353535353535353535353535353535353535353535353

}, 68-digit.

A prime number where all its digits are prime and every pair of consecutive digits is a prime. It is the only prime less than a googol with concatenation of two prime-digit primes 73 and 53.