Twin Prime Conjecture Proof

Steve One · 2018-02-25, 18:21

TWIN PRIME CONJECTURE PROOF:

1. Unless 'twin prime' every twin prime possibilty, (11/13 41/43
71/73 etc) (17/19 47/49 77/79 etc)and(29/31 59/61 89/91)
has a lowest prime factor of 7 or above. Eg. 119/121 has
factors of 7 11 and 17, therefore it's lowest prime factor is 7.
Lowest prime factors are all that we use.

2. If twin primes end, then necessarilly, there exists a prime(n)
that closes the last possibility of a pair being twin prime:
By applying this prime in the series as 'lowest prime factor'
twin primes end, take it out, they go on. This would
necessarilly be so.

3. PRIME(1) = 7: PRIME(2) = 11 etc.

(Prime(1) - 2) / Prime(1)) × ((Prime(2) - 2)/ Prime(2)..........
... × (Prime(n) - 2) / Prime(n)...would have to equal zero if a
greatest prime number left zero gaps 'after' first position
placing as final lowest prime factor of a twin prime
possibilty.

5/7 × 9/11 × 11/13 × 15/17.....× (n - 2)/n) will never equal
zero. This is the number of 'gaps' (twin primes) left on
29/31 59/61 89/91 etc for example.

4. The equation has 'primes up to..' multiplied together,
dividing 'primes minus 2, up to..' multiplied together.
This cannot equal zero/leave zero gaps.

science_man_88 · 2018-02-25, 21:03

Quote:

Originally Posted by Steve One

TWIN PRIME CONJECTURE PROOF:

1. Unless 'twin prime' every twin prime possibilty, (11/13 41/43
71/73 etc) (17/19 47/49 77/79 etc)and(29/31 59/61 89/91)
has a lowest prime factor of 7 or above. Eg. 119/121 has
factors of 7 11 and 17, therefore it's lowest prime factor is 7.
Lowest prime factors are all that we use.

2. If twin primes end, then necessarilly, there exists a prime(n)
that closes the last possibility of a pair being twin prime:
By applying this prime in the series as 'lowest prime factor'
twin primes end, take it out, they go on. This would
necessarilly be so.

3. PRIME(1) = 7: PRIME(2) = 11 etc.

(Prime(1) - 2) / Prime(1)) × ((Prime(2) - 2)/ Prime(2)..........
... × (Prime(n) - 2) / Prime(n)...would have to equal zero if a
greatest prime number left zero gaps 'after' first position
placing as final lowest prime factor of a twin prime
possibilty.

5/7 × 9/11 × 11/13 × 15/17.....× (n - 2)/n) will never equal
zero. This is the number of 'gaps' (twin primes) left on
29/31 59/61 89/91 etc for example.

4. The equation has 'primes up to..' multiplied together,
dividing 'primes minus 2, up to..' multiplied together.
This cannot equal zero/leave zero gaps.

Conveniently missed 23,25 as a "possibility". lowest prime factor ... 5.

LaurV · 2018-02-26, 04:30

1. How about "9 and 11", "13 and 15", "25 and 27", etc...?
2. Oh, you don't like numbers ending in 5? How about "31 and 33", or "51 and 53", etc...?
3. When you say "lowest prime factors", keep in mind that this can be huuuuuuge... How about consecutive odd numbers ending in 1, 3, 7, 9, which are not divisible by 3, 5, 7, 11, 17, and not prime either? (such pair can be easily computed with modular calculus, even with a "lowest prime factor" of thousands of digits). That product you compute, is an infinite product, and it is always zero. As is the product for all primes p, of (p-2)/p which is a number under unit.

axn · 2018-02-26, 05:00

Quote:

Originally Posted by Steve One

1. Unless 'twin prime' every twin prime possibilty, (11/13 41/43
71/73 etc) (17/19 47/49 77/79 etc)and(29/31 59/61 89/91)
has a lowest prime factor of 7 or above. Eg. 119/121 has
factors of 7 11 and 17, therefore it's lowest prime factor is 7.
Lowest prime factors are all that we use.

Why do you start at 7? Hmmm... So you're considering only twin "possibilities" of the for 30n+12+/-1, 30n+18+/-1 and 30n+/-1, which, by construction would not have factors of 2,3 or 5. Cool. But you could've made it simpler and just stuck with 6n+/-1 form and used factors of 5,7,11,... But, whatever.

Quote:

Originally Posted by Steve One

2. If twin primes end, then necessarilly, there exists a prime(n)
that closes the last possibility of a pair being twin prime:
By applying this prime in the series as 'lowest prime factor'
twin primes end, take it out, they go on. This would
necessarilly be so.

Whoa, there! Not so fast. Even if there are only finite number of twin primes, that doesn't mean that there are only a finite number of twin prime "possibilities". In fact, there is an infinite number of them in each series after the "last" twin prime. Therefore, there is no last prime(n) that "closes the last possibility". We have an infinite number of primes to choose from to close the infinite number of possibilities.

Steve One · 2018-02-26, 12:05

Quote:

Originally Posted by science_man_88

Conveniently missed 23,25 as a "possibility". lowest prime factor ... 5.

Multiples of 2, 3 and 5 are not included because they are instantly known as not possible. It serves no purpose to include them. I did not say anything was finite, only contained within the 3 paired series.

science_man_88 · 2018-02-26, 12:30

Quote:

Originally Posted by Steve One

Multiples of 2, 3 and 5 are not included because they are instantly known as not possible. It serves no purpose to include them.

Same could said for all primes under 1 million ...

Steve One · 2018-02-26, 12:41

I don't actually know what you mean by that.

CRGreathouse · 2018-02-26, 15:26

You're going to have to make your proof more formal before you discover that your mistake is that you've proved

Theorem: For any x, there are infinitely many pairs (p, p+2) such that neither p nor p+2 has a prime divisor <= x.

instead of

Conjecture: There are infinitely many pairs (p, p+2) such that neither p nor p+2 has a prime divisor <= sqrt(p+2).

This is the usual mistake to make when attempting a proof of the twin prime conjecture, so don't feel too bad.

Steve One · 2018-02-26, 16:46

I don't see where l have even mentioned square roots. Nothing yet has been said to disprove what l wrote. Please show where specifically an error occurs.

science_man_88 · 2018-02-26, 16:56

Quote:

Originally Posted by Steve One

I don't see where l have even mentioned square roots. Nothing yet has been said to disprove what l wrote. Please show where specifically an error occurs.

The sqrt part is reference to the conjecture you say you've proved, not the one you have.

CRGreathouse · 2018-02-26, 17:29

Quote:

Originally Posted by Steve One

Nothing yet has been said to disprove what l wrote. Please show where specifically an error occurs.

Not worth my time, sorry. Maybe someone else will walk you through the mistake(s) in your proof.

2018-02-25, 18:21	#1
Steve One Feb 2018 2²·3² Posts	Twin Prime Conjecture Proof TWIN PRIME CONJECTURE PROOF: 1. Unless 'twin prime' every twin prime possibilty, (11/13 41/43 71/73 etc) (17/19 47/49 77/79 etc)and(29/31 59/61 89/91) has a lowest prime factor of 7 or above. Eg. 119/121 has factors of 7 11 and 17, therefore it's lowest prime factor is 7. Lowest prime factors are all that we use. 2. If twin primes end, then necessarilly, there exists a prime(n) that closes the last possibility of a pair being twin prime: By applying this prime in the series as 'lowest prime factor' twin primes end, take it out, they go on. This would necessarilly be so. 3. PRIME(1) = 7: PRIME(2) = 11 etc. (Prime(1) - 2) / Prime(1)) × ((Prime(2) - 2)/ Prime(2).......... ... × (Prime(n) - 2) / Prime(n)...would have to equal zero if a greatest prime number left zero gaps 'after' first position placing as final lowest prime factor of a twin prime possibilty. 5/7 × 9/11 × 11/13 × 15/17.....× (n - 2)/n) will never equal zero. This is the number of 'gaps' (twin primes) left on 29/31 59/61 89/91 etc for example. 4. The equation has 'primes up to..' multiplied together, dividing 'primes minus 2, up to..' multiplied together. This cannot equal zero/leave zero gaps.

2018-02-26, 12:41	#7
Steve One Feb 2018 2²×3² Posts	Primes under 1 million I don't actually know what you mean by that.

2018-02-26, 15:26	#8
CRGreathouse Aug 2006 5,987 Posts	You're going to have to make your proof more formal before you discover that your mistake is that you've proved Theorem: For any x, there are infinitely many pairs (p, p+2) such that neither p nor p+2 has a prime divisor <= x. instead of Conjecture: There are infinitely many pairs (p, p+2) such that neither p nor p+2 has a prime divisor <= sqrt(p+2). This is the usual mistake to make when attempting a proof of the twin prime conjecture, so don't feel too bad.

2018-02-26, 16:46	#9
Steve One Feb 2018 100100₂ Posts	I don't see where l have even mentioned square roots. Nothing yet has been said to disprove what l wrote. Please show where specifically an error occurs. Last fiddled with by Steve One on 2018-02-26 at 16:51 Reason: Missed out some writing

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2018-02-26, 04:30	#3
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 10,273 Posts	1. How about "9 and 11", "13 and 15", "25 and 27", etc...? 2. Oh, you don't like numbers ending in 5? How about "31 and 33", or "51 and 53", etc...? 3. When you say "lowest prime factors", keep in mind that this can be huuuuuuge... How about consecutive odd numbers ending in 1, 3, 7, 9, which are not divisible by 3, 5, 7, 11, 17, and not prime either? (such pair can be easily computed with modular calculus, even with a "lowest prime factor" of thousands of digits). That product you compute, is an infinite product, and it is always zero. As is the product for all primes p, of (p-2)/p which is a number under unit.