What is the next number in the sequence? (not a trick)

[Gleb Gamow]

31, 37, 53, 71. 73, ...

And please state why.

Hint provided after at least five incorrect answers.

[aarons6]

those are all prime numbers so its 79

but since there are 3 missing in the middle maybe you want  97 101?

[Gleb Gamow]

those are all prime numbers so its 79

but since there are 3 missing in the middle maybe you want  97 101?

Yes, it's a prime, but has nothing to do with the number of numbers missing. BTW, one of your three guesses is correct.

Here's a sequence applying the same rules: 353, 373, 503, 521, ...

What's the next number?

[Gleb Gamow]

Okay, I'll give the answer since I just found the ONLY other source on the internet offering up this sequence: https://oeis.org/A160337 (follow link to uncover the answer and why).

Now, why doesn't The OEIS Foundation accept bitcoin donations?

In the mean time, I'm goin' to devise another sequence, and if it's never been expressed before, I'm naming it after myself: Bruno's Primes.  

Edit: Looks like I was beat to the punch with that idea as well: [1, 2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 113, 131, 137, 173, 311, 313, 317, 373, 1373, 3137]: http://www.mersenneforum.org/showthread.php?t=20246

I was just about to have you guess the number 1373, but I discovered that there's only one number left to complete the sequence. Damn!

[SmartIphone]

The next number must me 35, please let me know if i am right.

[Gleb Gamow]

The next number must me 35, please let me know if i am right.

If you're answering the question posed in the OP, the answer was 101.