Question

Help. I am trying to find complete sets of composites (4-dingt numbers ending in 1,3,7, or 9) that can reach past 200,000, for example.
4553, 14553, 24553, 34553...... etc. all the way until one is prime. Also is it possible for no primes to be ending in any 4-digit number ending in 1,3,7, or 9. I find it hard.

Answer 1

I'm not sure I understand what you're after.
104729 is a prime number...

Answer 2

Oh I see. 4729 is a prime and so your list ends there...
4553 goes to 64553, which is prime. You want a four digit number that becomes a prime after passing 200000.

Answer 3

Like 7821?

Answer 4

1037, 7821, and 9647 are the only ones that get higher than 200,000.

Answer 5

For four digit numbers ending in 1, 3, 7, or 9 but becoming prime only after surpassing 200000, I got:

1037 -> 201037
1989 -> 221989
2513 -> 232513
5489 -> 235489
7439 -> 217439
7461 -> 477461
7821 -> 207821
8267 -> 238267
9647 -> 209647

Note, A -> B means 4 digit number A is initially prime at B, when we change A in the following way: start with a four digit number ending in 1, 3, 7, or 9, and then prepend it with a number in the range [0, ..., <some really large number>], e.g.:

1037, 11037, 21037, ..., 9999991037

Answer 6

@doc.brown

Answer 7

Thanks you so much, where did you manage to get these numbers. I was also wondering if there is a record higher that "7461". Or if there is another number like that that has no primes at all. Thanks, once again.

Answer 8

By the ways, I knew of "7461" and "2513" as well as "10337" which I discovered first. But Thanks for the other numbers, now I know that "2513" is not unique. Did you test every 4-dig. number, Or are these all the numbers that pass?

Answer 9

I made a program to test every four digit number ending in 1, 3, 7 or 9.

Answer 10

So there will be no higher record than 7461, right?