Counting Goldbach Prime Pairs Up To...

[Steve One]

Goldbach Prime Pairs Up To 8282 = (91squared+1), both numbers on number line (1+n30).
Others from (13+n30) + (19+n30) not counted.

(Primes 7 to 61, each minus 2, multiplied together) divided by (Primes 7 to 61, multiplied together) × ((Primes 67 to 89(91 isn't prime), each minus 1, multiplied together) divided by (Primes 67 to 89) × (8282-1)÷60) = 28.2098. There are 28 pairs of prime numbers on number line (1 + n30) that when added = 8282

Or, (5/7 × 9/11 × 11/13....×(prime n1 minus2)/(prime n)) × (66/67 × 70/71....×(prime n minus1)/prime n) × (N - 1)/60 which equals

0.22126 × 0.92387 × 138 = 28.20980

N = 8282.
n = prime preceding square root of(N - 1)/60 which is 89.
n1 = prime preceding square root of (N - 1)/120 which is 61.

Right but wrong?

[science_man_88]

Originally Posted by Steve One

Goldbach Prime Pairs Up To 8282 = (91squared+1), both numbers on number line (1+n30).
Others from (13+n30) + (19+n30) not counted.

(Primes 7 to 61, each minus 2, multiplied together) divided by (Primes 7 to 61, multiplied together) × ((Primes 67 to 89(91 isn't prime), each minus 1, multiplied together) divided by (Primes 67 to 89) × (8282-1)÷60) = 28.2098. There are 28 pairs of prime numbers on number line (1 + n30) that when added = 8282

Or, (5/7 × 9/11 × 11/13....×(prime n1 minus2)/(prime n)) × (66/67 × 70/71....×(prime n minus1)/prime n) × (N - 1)/60 which equals

0.22126 × 0.92387 × 138 = 28.20980

N = 8282.
n = prime preceding square root of(N - 1)/60 which is 89.
n1 = prime preceding square root of (N - 1)/120 which is 61.

Right but wrong?

Claims

1. Goldbach partitions congruent to 1 modulo 30<8282 =28
2. the n-th prime.

Oh , and n=11 not 89 and n1= 7 based on those definitions.

[CRGreathouse]

Thank you for attempting to explain.

Originally Posted by science_man_88

Goldbach partitions congruent to 1 modulo 30<8282 =28

I assume that by "Goldbach partitions" you mean pairs (p,q) of primes which add up to a given even number. When you say congruent to 1 mod 30, do you mean that both primes are 1 mod 30? And then when you write "<8282=28", what does that mean? Something like "There are 28 Goldbach partitions of 8282 where both primes are 1 mod 30"? (I count 26, though.)

Originally Posted by science_man_88

the n-th prime.

Steve has some sort of product which has the \(\prod\) parts you suggest, but it looks like he has 8281/60 instead of 90^2/60. I find it somewhat inscrutable because the product with 8281/60 gives
29.239147
while the product you have gives
28.600059
and the product using his partial work "0.22126 × 0.92387 × 138" suggests 8280 which gives
29.235615
(all numbers rounded to six digits).

Probably this is all a mess because Steve doesn't know what he's doing. But if we pretend he does we could ask: what is this supposed to mean? It seems to be some sort of prediction of the density or count of the primes on some interval, but which and what exactly is it?

Originally Posted by science_man_88

Oh , and n=11 not 89 and n1= 7 based on those definitions.

More little mistakes showing that he doesn't know what he's doing (or is trolling, I suppose).

[science_man_88]

Originally Posted by CRGreathouse

Thank you for attempting to explain.


I assume that by "Goldbach partitions" you mean pairs (p,q) of primes which add up to a given even number. When you say congruent to 1 mod 30, do you mean that both primes are 1 mod 30? And then when you write "<8282=28", what does that mean? Something like "There are 28 Goldbach partitions of 8282 where both primes are 1 mod 30"? (I count 26, though.)



Steve has some sort of product which has the \(\prod\) parts you suggest, but it looks like he has 8281/60 instead of 90^2/60. I find it somewhat inscrutable because the product with 8281/60 gives
29.239147
while the product you have gives
28.600059
and the product using his partial work "0.22126 × 0.92387 × 138" suggests 8280 which gives
29.235615
(all numbers rounded to six digits).

Probably this is all a mess because Steve doesn't know what he's doing. But if we pretend he does we could ask: what is this supposed to mean? It seems to be some sort of prediction of the density or count of the primes on some interval, but which and what exactly is it?



More little mistakes showing that he doesn't know what he's doing (or is trolling, I suppose).

I replaced "Goldbach Prime pair" with Goldbach partition because that's how I translate it http://mathworld.wolfram.com/GoldbachPartition.html I replaced "up to" with < and left 8282 as it was the =28 came from another part ( claim about 8282 itself I think) he calls a linear integer polynomial, a number line. Both in the pair have to be 1 modulo 30. I may have confused where his parentheses are, but 91^2=8281 so maybe also a typo on my part. And technically the denominator products as I gave them, multiply to a primorial.

[CRGreathouse]

OK, but you don't know, for example, what region this formula is supposed to count primes over?

[science_man_88]

Originally Posted by CRGreathouse

OK, but you don't know, for example, what region this formula is supposed to count primes over?

No, because the thread title and first sentence, don't align with a statement made later. Thread title and first sentence say up to, other part says 28 just for 8282

[Steve One]

Originally Posted by Steve One

Goldbach Prime Pairs Up To 8282 = (91squared+1), both numbers on number line (1+n30).
Others from (13+n30) + (19+n30) not counted.

(Primes 7 to 61, each minus 2, multiplied together) divided by (Primes 7 to 61, multiplied together) × ((Primes 67 to 89(91 isn't prime), each minus 1, multiplied together) divided by (Primes 67 to 89) × (8282-1)÷60) = 28.2098. There are 28 pairs of prime numbers on number line (1 + n30) that when added = 8282

Or, (5/7 × 9/11 × 11/13....×(prime n1 minus2)/(prime n)) × (66/67 × 70/71....×(prime n minus1)/prime n) × (N - 1)/60 which equals

0.22126 × 0.92387 × 138 = 28.20980

N = 8282.
n = prime preceding square root of(N - 1)/60 which is 89.
n1 = prime preceding square root of (N - 1)/120 which is 61.

Right but wrong?

Interestingly, l did make a massive mistake.
Not,
n = prime preceding square root of(N - 1)/60 which is 89.
n1 = prime preceding square root of (N - 1)/120 which is 61.

But,
Should be n = ..................................(N - 1)
Should be n1 = ................................(N -1)/2
Interesting, that you didn't notice that. But then again maybe not.
Your ganging up is quite funny. I don't actually dislike notation. I just don't know it and didn't appreciate making out that it was godly and putting down my simplistic notation.
You guys remind me of my days playing Pool for a living on the road, The Colour Of Money/Hustler style in America in the early nineties. People like you would show off with your 2,000 dollar+ cues, then l'd get one out of the rack and batter you with it, leaving you pennyless. Do you get the analogy? Probably not. Regardless of how crap l've written everything, the fundamentals are correct. It's called intelligence, except the Collatz proof, that's just pure genius. Whereas yours is called being able to remember what somebody else told you, then just regurgitating it. Wow! That's amazing!

[science_man_88]

Originally Posted by Steve One

Interestingly, l did make a massive mistake.
Not,
n = prime preceding square root of(N - 1)/60 which is 89.
n1 = prime preceding square root of (N - 1)/120 which is 61.

But,
Should be n = ..................................(N - 1)
Should be n1 = ................................(N -1)/2
Interesting, that you didn't notice that. But then again maybe not.
Your ganging up is quite funny. I don't actually dislike notation. I just don't know it and didn't appreciate making out that it was godly and putting down my simplistic notation.
You guys remind me of my days playing Pool for a living on the road, The Colour Of Money/Hustler style in America in the early nineties. People like you would show off with your 2,000 dollar+ cues, then l'd get one out of the rack and batter you with it, leaving you pennyless. Do you get the analogy? Probably not. Regardless of how crap l've written everything, the fundamentals are correct. It's called intelligence, except the Collatz proof, that's just pure genius. Whereas yours is called being able to remember what somebody else told you, then just regurgitating it. Wow! That's amazing!

you probably don't know intellect from intelligence.

[CRGreathouse]

Originally Posted by Steve One

Regardless of how crap l've written everything, the fundamentals are correct.

I'm glad to hear you think that. Could you clarify the points I've asked about? To wit:

• What is being counted, exactly? Pairs of primes which sum to N?
• Does your formula give the exact count or an approximate count?
• If approximate, in what sense? A heuristic? An asymptotic (relative error tends to 0 with N)? Something else?
• Your formula treats the primes from 7 to 61 differently from the primes from 67 to 89. If we use some other N, how do we determine which primes get -1 and which get -2?
• Does this formula work only for numbers N which are one more than a square, or does it work for more general numbers?