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?

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Comments

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.

Siddhartha Srivastava - 5 years, 7 months ago

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

Arihant Samar - 5 years, 7 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).

Siddhartha Srivastava - 5 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$