🧵 Fun trivial proof of at least one prime
Anonymous at Tue, 19 Mar 2024 01:37:03 UTC No. 16085822
The arithmetic progression of the form 3n+1 contains at least one prime.
Assume it doesn't, then for any natural a, b, (3a+2)(3b+2)=3c+1 so that there is a bijection between naturals c and (a, b).
But notice that (3a+2)(3b+2)=((3a+1)+1)((3b+1+1))=(
Notice something weird?
You guessed it if you look at mod 3, the remainder (number not factored by x or y or z or w) tends to a very big number the more such "nesting" is performed on the form (3n+2).
Brilliant! In fact this proof works for every prime p and 0 < q <p for the progression pn+q.
I won't tell you the details of course because I don't want to spoil anything (hint: just decompose a progression into corresponding multiples of progressions(
Anonymous at Tue, 19 Mar 2024 01:47:19 UTC No. 16085829
Implicitly, [math]\alpha(n)=3n+1[/math] is and endomorphism on the natural numbers and so is [math]\phi(a, b)=(3a+2)(3b+2)[/math] so that the composition [math]\alpha^{-1}\circ\phi[/math] is a bijection.
Then there's nesting [math]\phi=(\phi+1)(\phi+1)[/math]
And finally there's a contradiction since there is a very big margin in the image of [math]\alpha^{-1}\circ\phi[/math] once nesting is applied.
Hence there is at least one prime number.
Tadaa..
Anonymous at Tue, 19 Mar 2024 01:50:18 UTC No. 16085833
>>16085829
Uhhh I meant a surjection
Anonymous at Tue, 19 Mar 2024 02:42:09 UTC No. 16085899
>Numbers that are +1 or -1 an even number have a chance of being prime.
Holy shit
Anonymous at Tue, 19 Mar 2024 11:28:13 UTC No. 16086346
>>16085899
If you are so smart why don't you show me there is a prime number in any good irreducible polynomial?
Right, you can't, because you are a retarded nigger who doesn't understands the subjwct
bodhi at Tue, 19 Mar 2024 11:42:50 UTC No. 16086360
>>16086346
Cope, I have achieved more than you
Anonymous at Tue, 19 Mar 2024 11:53:29 UTC No. 16086375
>>16086360
I don't even know you, I messaged the other dude.
You are just another uneducated schizo on this board who misreads and bullies people with a fictitious sense of superiority.
Know your place
bodhi at Tue, 19 Mar 2024 11:55:31 UTC No. 16086378
>>16086375
post your thesis first, then we can talk
Anonymous at Tue, 19 Mar 2024 12:02:49 UTC No. 16086384
Wait til this nigga learns about 6n+1 and stops checking even numbers for primes
Anonymous at Tue, 19 Mar 2024 13:06:31 UTC No. 16086455
>>16086384
You are a worthless undergrad who thinks I will give him a free proof of at least one prime in 6n+1
Go back to doing your homework retarded worthless talentless children
>>16086378
You don't have a thesis because you are this retarded /sci/ schizophrenia who keeps making up shit here, either way I don't share my personal info to some retarded strangers here so you'll have to contact me personally
Barkon at Tue, 19 Mar 2024 15:13:11 UTC No. 16086600
>>16086455
Mathematician here. Seems to me you've lost. Better stop posting before you embarrass yourself further
Anonymous at Tue, 19 Mar 2024 15:16:22 UTC No. 16086606
>>16086455
>at least one prime in 6n+1
Set n=1
Garrote at Tue, 19 Mar 2024 15:35:27 UTC No. 16086620
wtf 7 is prime
Anonymous at Tue, 19 Mar 2024 15:36:39 UTC No. 16086623
>>16086606
op btfo
Anonymous at Tue, 19 Mar 2024 17:13:14 UTC No. 16086747
Anonymous at Tue, 19 Mar 2024 17:25:45 UTC No. 16086759
>>16085822
>proof by contradiction
You haven't solved the problem
Anonymous at Wed, 20 Mar 2024 07:34:03 UTC No. 16087710
>>16085822
Damn so 7 is a prime
Anonymous at Wed, 20 Mar 2024 09:27:38 UTC No. 16087805
>>16085822
let me clean up your mess so you can see the mistakes
>assume 3c+1 is not prime
>then for some a,b we can nontrivially factor either 3c+1 = (3a+1)(3b+1) or 3c+1=(3a+2)(3b+2)
>either way, a,b are each smaller than c
>now assume 3a+1, 3b+1 are not prime and repeat
>continue until we reach a=b=0
>now our last “c” must equal 4
I’m not sure what this says about the initial number
bodhi at Thu, 21 Mar 2024 06:31:13 UTC No. 16089126
OP sure got BTFO'd hard