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Forum: Number Theory Discussion Group 2020-10-27, 19:44
Replies: 27
Views: 5,512
Posted By R2357
Smile Did you analyse the way Possible Prime Positions...

Did you analyse the way Possible Prime Positions are taken away in patterns of p# (and I'm not even talking about the composites by primes higher than p)

2 takes away each of its multiples (as...
Forum: Number Theory Discussion Group 2020-10-27, 06:44
Replies: 27
Views: 5,512
Posted By R2357
Question It looks like "we" are certain that something is wrong...

So, if I understand, "we" believe that there exist a counter-example for the 2nd Hardy-Littlewood conjecture, which is already surprising!

But even more surprising is that we think that it's...
Forum: Number Theory Discussion Group 2020-10-26, 17:07
Replies: 27
Views: 5,512
Posted By R2357
I don't understand what you really mean by "human...

I don't understand what you really mean by "human intuition", when we look at the primes from 1 to 3159, this makes more than 14% of the natural numbers, the non-multiples of one and two digit...
Forum: Number Theory Discussion Group 2020-10-23, 19:20
Replies: 27
Views: 5,512
Posted By R2357
Cool Okay, in my calculation, I overlooked the fact...

Okay, in my calculation, I overlooked the fact that numbers congruent to a composite up to 53# divisible by primes from 59 onwards, modulo 53# may be prime, mea culpa :|

But still,...
Forum: Number Theory Discussion Group 2020-10-23, 18:12
Replies: 27
Views: 5,512
Posted By R2357
Question Co prime doesn't mean prime, and I still don't...

Co prime doesn't mean prime, and I still don't understand why the odds are to think that the conjecture is wrong, okay, it's incompatible with the first, but there is no particular reason to think...
Forum: Number Theory Discussion Group 2020-10-23, 14:11
Replies: 27
Views: 5,512
Posted By R2357
Smile Answer

Simply because in any sequence 53#*n to 53#*n+1, all the numbers that are congruent to x*{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53} modulo 53# will be divisible by a prime up to 53....
Forum: Number Theory Discussion Group 2020-10-23, 08:11
Replies: 27
Views: 5,512
Posted By R2357
Sequence of 3159 numbers containing 447 primes

Anyway, if there indeed is such a sequence, then the first or the occurrence will have been reached by 32 589 158 477 190 044 730, thus way below the lower band of 10^174.
Forum: Number Theory Discussion Group 2020-10-22, 16:35
Replies: 27
Views: 5,512
Posted By R2357
But the region where they are searching is over...

But the region where they are searching is over 10^174, so, if we want to find within a sequence of 3159, 447 prime numbers, that means that the interval, this high, must contain even less composite...
Forum: Number Theory Discussion Group 2020-10-22, 14:07
Replies: 27
Views: 5,512
Posted By R2357
Question 2nd Hardy-Littlewood conjecture

Hello,

I've looked at the way primes behave in sequences which have a primorial length and, as I mentionned a few weeks ago, I came across the 2nd Hardy-Littlewood conjecture, which was...
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