Question

How many different four-digit, positive integers are there where each digit is a prime number?

Answer 1

Plenty...
http://primes.utm.edu/lists/small/1000.txt

Answer 2

well u have 4 one-digit prime number
2,3,5,7
ur four-digit number must include this 4
lol my english is not well
@KingGeorge

Answer 3

That's going to take awhile, but that's many of them, there's the 8000's and 9000' too though

Answer 4

1 is a prime # too @mukushla

Answer 5

Think... No?

Answer 6

Mukushla is on the right track. There are 4 distinct one-digit primes. In a 4 digit number, there are 4 digits. If each digit must be prime, then you have 4 options for each digit.

Hence, you have \(4^4\) 4-digit positive numbers with a prime for each digit.

Answer 7

so is it 790

Answer 8

no... How did you get that?

Answer 9

@agentx5
1 is not prime

Answer 10

It's not? Hmm, my bad then... Unless my count is wrong, there are:

4, one-digit primes
21, two-digit primes
137, three-digit primes

So... make the computer do a parabolic curve fit...

\[f(x)=\frac{99}{2}x^2-\frac{263}{2}x+86\]

So...

\[f(x)=\frac{99}{2}(4)^2-\frac{263}{2}(4)+86=352\]

This would be my guess as what to expect, in reality though it probably is off, how much? I don't know outside of seeing a longer list and counting.

Answer 11

err that should say f(4)

I used "curve fit (1,4) (2,21) (3,137)"

Answer 12

You're approaching this problem completely wrong agent. We only have 4 numbers to choose from (2,3,5,7) and we have 4 digits to fill. Since we can repeat numbers, the solution is merely \[4\cdot4\cdot4\cdot4=4^4=256\]

Answer 13

We aren't looking for how many 4 digit numbers are prime themselves. We're looking for 4 digit numbers whose digits are prime.

Answer 14

That sounds easier, I'd go with what @KingGeorge said :-)

Answer 15

And yeah I see what you mean... not all prime, just the ones with prime digits, like a combination.

Answer 16

Just fyi, if my information is correct, there are actually 1061 4-digit numbers that are prime themselves.