Talk:Primefree sequence

I hav a couple questions that I think teh article should address:

1. obiously you can't examine every single term, so how can you be sure its primefree if the iniital terms are coprime?
2. is their a requirement that the initial terms be of simlar magnitude? could I have a1 = 4 and a2 = some big number like 165465485323?
3. can a Sylvester-like sequence be primefree?

Numerao 17:44, 20 September 2005 (UTC)

p.s. I know the example I give has primes at 11, 45, 66, 93... the famous Wilf-Hoffman example doesn't have it's first prime until 138, that kinda goes back to my first question.

I too am quite curious about your first and third questions, and I wish I could answer them. I've studied Sylvester-like sequences in connection with Znám's problem, and it seems to me that a primefree Sylvester-like sequence would be quite remarkable. Each new term you add is coprime to all the previous terms, making the odds of hitting a prime that much higher.

As for your second question, I think it's simply a matter of not casting too wide a net. As you've demonstrated, you know numbers are infinite. So if you're a mathematician looking to find a primefree sequence, you're more likely to make your initial terms be close to each other. Anton Mravcek 23:09, 21 September 2005 (UTC)

I've added an explanation of the first question to the article. The second question may take the article too far afield, but there's no such requirement (in fact, it would be easy to generate terms with very different magnitudes). The papers try to find minimal terms, so their terms tend to be similar in magnitude. Kuleebaba (talk) 17:22, 30 December 2007 (UTC)

Other primefree sequences

These sequences are also primefree sequences:

9*4^n-1

1*8^n+1

47*8^n+1

14*8^n-1

27*8^n-1

4*9^n-1

16*9^n-1

25*12^n-1

27*12^n-1

4*14^n+1

11*14^n+1

4*14^n-1

9*14^n-1

11*14^n-1

9*16^n-1

8*20^n+1

13*20^n+1

8*20^n-1

13*20^n-1

4*24^n-1

6*24^n-1

9*24^n-1

Why there seems to be no interest of them? 218.187.64.145 (talk) 18:45, 9 June 2023 (UTC)