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?

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestI 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.

Log in to reply

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

Log in to reply

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).

Log in to reply