# Prime filled with primes

1)Consider a 3-digit natural number abc.How many such 3-digit numbers are there such that ab,bc and ca are all prime?

2 )Consider a 3-digit natural number abc.How many such 3-digit numbers are there such that ab,bc and ca are all prime and abc is also prime?

Note: ab ,bc and ca are 2 digit numbers.It is not the multiplicative function.

This question is original.Can someone tell me how to solve this?

Note by Arihant Samar
2 years, 9 months ago

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I don't think there is any way other than taking a list of primes and checking each one.

Some things to speed up the process is to see is no digit can be even and/or 5.

Using this, some answers to b) are 317, 971, 137, 173, 197, and 719.

- 2 years, 9 months ago

Are the answers for part a) and b) the same?

- 2 years, 9 months ago

I don't know. You can check using a list of primes less than 1000.

Since there are a lower number of conditions in a) as compared to b), it seems very likely that more numbers should satisfy a).

- 2 years, 9 months ago