Talk:Primefree sequence
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I hav a couple questions that I think teh article should address:
- obiously you can't examine every single term, so how can you be sure its primefree if the iniital terms are coprime?
- is their a requirement that the initial terms be of simlar magnitude? could I have a1 = 4 and a2 = some big number like 165465485323?
- 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)
