[seqfan] Re: (no subject)
M. F. Hasler
oeis at hasler.fr
Thu Dec 7 19:41:35 CET 2017
On Wed, Dec 6, 2017 at 4:46 PM, <israel at math.ubc.ca> wrote:
> Naively one might expect: for any b > 0 there should be infinitely many a
> making it prime, and for any a > 0 there should be infinitely many b making
> it prime. But of course none of this is likely to be provable with current
> technology.
>
I was about to reply the same thing when Robert's message arrived.
Now let me give a complementary remark: sequence oeis.org/A113412
lists the number a(n) of such primes < 10^2^n and this seems to indicate
that a(n+1) / a(n) ~ 2 and actually a(n) >~ 2^(n+3) (">" for n > 7).
- Maximilian
PS: the "More terms from..." %Extension lines would make more
sense if changed to "a(m) through a(n) from ...", not only in A005109.
On Dec 6 2017, Hugo Pfoertner wrote:
>
> In the range 1<=a,b<=500 there are 2111 primes of this form. Large
>> examples: 1+(2^498)*(3^493) or 1+(2^994)*(3^993). Why should there be a
>> limit?
>>
>> On Wed, Dec 6, 2017 at 6:51 PM, Frank Adams-Watters wrote:
>>
>> Is https://oeis.org/A058383 (Primes of form 1+(2^a)*(3^b)) infinite?
>>>
>>
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