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Forum: Puzzles 2020-06-03, 04:58
Replies: 7
Views: 432
Posted By a1call
You are correct of course, but only iff,...

You are correct of course, but only iff, (generic)-you decide to exclude 1 from the definition of one or the other by some twisted logic but not both.:smile:

Google >> define coprime numbers >>...
Forum: Puzzles 2020-06-02, 19:01
Replies: 7
Views: 432
Posted By a1call
Thank you LaurV, But I actually new about that...

Thank you LaurV, But I actually new about that function.
One day in elementary school my geometry teacher asked if anyone could prove some particular theorem. I raised my hand described a valid...
Forum: GPU to 72 2020-06-01, 23:25
Replies: 7
Views: 184
Posted By a1call
https://www.theregister.com/2020/02/07/google_chro...

https://www.theregister.com/2020/02/07/google_chrome_blocking/

so https should be warning free
Forum: Puzzles 2020-06-01, 21:58
Replies: 7
Views: 432
Posted By a1call
We cross posted. I stand corrected on 1. But, I...

We cross posted. I stand corrected on 1. But, I still think it's a matter of convention and not logic.:smile:
ETA: In the same way 1 was considered to be a prime number at some point until someone...
Forum: Puzzles 2020-06-01, 21:14
Replies: 7
Views: 432
Posted By a1call
Do you mean include 0? Pari-gp code: ...

Do you mean include 0?

Pari-gp code:

counter=0
for(i=2,278,{
if(gcd(278,i)<2,counter=counter+1);
})
counter
Forum: Miscellaneous Math 2020-05-31, 04:30
Replies: 20
Views: 529
Posted By a1call
Thank you Paul. I know it is small potatoes, but...

Thank you Paul. I know it is small potatoes, but the size would be a top 10 (20 counting twins as double) if it were a twin prime which is what I am aiming for.
I have a virtual-box instance which...
Forum: Miscellaneous Math 2020-05-31, 04:16
Replies: 20
Views: 529
Posted By a1call
FTR the number was proven prime via PFGW by using...

FTR the number was proven prime via PFGW by using the -tp flag, FactorDB says "Too big to be tested at the moment." for N+1 proof. I am not sure how temporary is the "at the moment" if at all.:smile:
Forum: Miscellaneous Math 2020-05-30, 22:41
Replies: 20
Views: 529
Posted By a1call
A 79820 dd Prime example found using PFGW: ...

A 79820 dd Prime example found using PFGW:

(20577!-2652)/2652 (http://factordb.com/index.php?id=1100000001517259328)

Currently waiting for FactorDB to process the number.
Stay tuned if not...
Forum: Hardware 2020-05-28, 17:37
Replies: 6
Views: 431
Posted By a1call
Why wouldn't supercomputers made of clusters of...

Why wouldn't supercomputers made of clusters of PCs on any network, say internet work?
What is the difference in the architecture?

Is this just a fancy name for distributed computing such as...
Forum: Miscellaneous Math 2020-05-20, 06:21
Replies: 20
Views: 529
Posted By a1call
This version should work though not using/being a...

This version should work though not using/being a minimal n:

DHS-200-B Any given pair of twin primes q & p where p = q+2 can be expressed as (n! +/- k)/(k) for infinite integers n such that:
n >=...
Forum: Miscellaneous Math 2020-05-20, 05:53
Replies: 20
Views: 529
Posted By a1call
This is wrong. At least if the k has to be an...

This is wrong. At least if the k has to be an integer.
Will see of I can come up with a correct version.
To be continued ...
Forum: Miscellaneous Math 2020-05-20, 03:56
Replies: 20
Views: 529
Posted By a1call
DHS-200-A Any given pair of twin primes q & p...

DHS-200-A Any given pair of twin primes q & p where p = q+2 can be expressed as (n! +/- k)/(k) for infinite integers n such that:
n >= r where r is the greatest prime factor of (q+1)
&
k =...
Forum: Miscellaneous Math 2020-05-20, 02:59
Replies: 20
Views: 529
Posted By a1call
DHS-190-A There are infinitely many distinct...

DHS-190-A There are infinitely many distinct twin-coprimes-to-n! (Please see post #9 (https://www.mersenneforum.org/showpost.php?p=545647&postcount=9)) of the form (n! +/- k)/(k), since for all...
Forum: Miscellaneous Math 2020-05-19, 18:29
Replies: 20
Views: 529
Posted By a1call
DHS-180-A For any given factorial n! if (n! +/-...

DHS-180-A For any given factorial n! if (n! +/- k)/(k) are both positive integers which are both coprime to n! & (n! +/- k)/(k) < n^2, then (n! +/- k)/(k) are twin primes

To-be-continued ...:smile:
Forum: Miscellaneous Math 2020-05-19, 18:11
Replies: 20
Views: 529
Posted By a1call
DHS-170-A For any given factorial n! greater than...

DHS-170-A For any given factorial n! greater than 4!, let v be the valuation of prime factor q of n!, where q >=5

Then we know that one of the (n! +/- q^v)/(q^v) will have a valuations of q that...
Forum: Miscellaneous Math 2020-05-19, 03:12
Replies: 20
Views: 529
Posted By a1call
DHS-160-A For any given factorial n! greater than...

DHS-160-A For any given factorial n! greater than 2!, let v be the valuation of prime factor 3 of n!.

Then we know that one of the (n! +/- 3^v)/(3^v) will have a valuations of 3 that is 0 and the...
Forum: Miscellaneous Math 2020-05-18, 14:53
Replies: 20
Views: 529
Posted By a1call
FTR As of the time of this posting a...

FTR As of the time of this posting a Google-Search for "Extended Factorial Primes" (with quotes) returns no results. Not even this thread which is unusual.
As of the time of this posting a...
Forum: Miscellaneous Math 2020-05-17, 19:02
Replies: 20
Views: 529
Posted By a1call
To clarify the fruit- world- word-salad that is...

To clarify the fruit- world- word-salad that is "DHS-100-A" (with or without quotes), consider the following numeric example for n = 11:

n! = 2^8 * 3^4 * 5^2 * 7^1 * 11^1

Now for any k = 2^a *...
Forum: Miscellaneous Math 2020-05-17, 15:58
Replies: 20
Views: 529
Posted By a1call
On yet another spin-off proving that there exists...

On yet another spin-off proving that there exists a distinct twin prime of the form (n!+/-k)/k for an integer n greater than any given integer will prove the infinitude of twin primes.

ETA ...
Forum: Miscellaneous Math 2020-05-17, 15:24
Replies: 20
Views: 529
Posted By a1call
Here is a relevant discussion for reference: ...

Here is a relevant discussion for reference:

https://math.stackexchange.com/questions/1794286/factorial-and-primorial-twin-primes

FTR I don't think that perhaps it should not be an "open...
Forum: Miscellaneous Math 2020-05-17, 13:38
Replies: 20
Views: 529
Posted By a1call
A search for "!" (Without the quotes) in the...

A search for "!" (Without the quotes) in the Top-5k database only returns factorial-primes with k = 1. So I assume we can conclude that there are no primes of the format with k>1 in the Top-5k....
Forum: Miscellaneous Math 2020-05-16, 19:26
Replies: 20
Views: 529
Posted By a1call
Here is a nice little spin-off: Take any...

Here is a nice little spin-off:

Take any factorial n!

Find a PRP in the format:

p = (n! +/- k)/k

Where for largest prime factor q of k you have q <= n
Forum: Miscellaneous Math 2020-05-16, 18:50
Replies: 20
Views: 529
Posted By a1call
I think we better change it to => 9!, Since the...

I think we better change it to => 9!, Since the valuation of 2 and 3 would have to be greater than 1 in the factorial.

This also means that any n= 2^a* 3^b*m
For integers a, b and m where they...
Forum: Miscellaneous Math 2020-05-16, 17:33
Replies: 20
Views: 529
Posted By a1call
Well if it's not a factorial the no fraction part...

Well if it's not a factorial the no fraction part won't hold (or the coprime part). If you don't mind that you can replace the 2's and the 3's with any value.

Only Factorials can ensure both...
Forum: Miscellaneous Math 2020-05-16, 16:38
Replies: 20
Views: 529
Posted By a1call
Unity Working for any Factorial

With no fractions along the way. Every intermediary value after division is coprime to the factorial, regardless of its size.
Please see the image.
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