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Old 2015-11-24, 14:15   #1
Ale
 
Nov 2015

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Question This simple algorithm incomplete can only calculate prime numbers?

Ciao,


3 x 3 x 2 x 4 = 72 -1 = 71 (is a prime number)

now 5:

3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 = 25920 -1 = 25919 (is a prime number)

.

now 6 :

3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 = 223948800 -1 = 223948799 ( is a prime number)

ho isolato il
2 x 4


now 7 :


3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 x 3 x 4 x 5 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 = 3047495270400000 -1 = 3047495270399999 ( is a prime number)

Do you understand the mechanism? then work to the 8 -9-10 ........ should be all primes larger.
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Old 2015-11-24, 15:57   #2
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Quote:
Originally Posted by Ale View Post
Ciao,


3 x 3 x 2 x 4 = 72 -1 = 71 (is a prime number)

now 5:

3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 = 25920 -1 = 25919 (is a prime number)

.

now 6 :

3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 = 223948800 -1 = 223948799 ( is a prime number)

ho isolato il
2 x 4


now 7 :


3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 x 3 x 4 x 5 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 = 3047495270400000 -1 = 3047495270399999 ( is a prime number)

Do you understand the mechanism? then work to the 8 -9-10 ........ should be all primes larger.
I like to find patterns and all I see for the most part is that they will always produce numbers that have remainder of 5 when dividing by 6.
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Old 2015-11-24, 16:28   #3
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Quote:
Originally Posted by Ale View Post
then work to the 8 -9-10 ........ should be all primes larger.
Why?
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Old 2015-11-24, 16:39   #4
Ale
 
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I'm italian and not speak very well english, but because I can not test them are too large after 7, they have 23 decimals, for example 8
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Old 2015-11-24, 17:18   #5
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Quote:
Originally Posted by Ale View Post
I'm italian and not speak very well english, but because I can not test them are too large after 7, they have 23 decimals, for example 8
so far I have the second is the first squared times 5 the third is the second squared over 3 the fourth appears to be the third squared times 35/576. so what am I missing ?

translated with google: finora, ho il secondo è le prime volte quadrato 5, il terzo è il secondo quadrato superiore a 3, il quarto sembra essere la terza tempi quadrato 35/576. così che cosa mi manca?
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Old 2015-11-24, 17:58   #6
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this is 7

3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 x 3 x 4 x 5 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 = 3047495270400000 -1 = 3047495270399999

now 8 is:


3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 x 3 x 4 x 5 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 x3 x 2 x 4 x 5 x 6 x 3 x 4 x 5 x 6 x 3 x ? 6 x 7 x 8 = n - 1 = prime number
or
x ? 5 x 6 x 7 x 8 = n - 1 = prime number

I can not test the true mechanism , but i think ( you see 4 x 5 x 6 , 3 times , and the number moltiplication 3 always after a series of numbers ) , i think that ,in this mechanism there is peralps hide one algorithm particular for to find a prime numbers.

Last fiddled with by Ale on 2015-11-24 at 18:03
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Old 2015-11-24, 18:08   #7
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Quote:
Originally Posted by Ale View Post
this is 7

3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 x 3 x 4 x 5 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 = 3047495270400000 -1 = 3047495270399999

now 8 is:


3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 x 3 x 4 x 5 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 x3 x 2 x 4 x 5 x 6 x 3 x 4 x 5 x 6 x 3 x ? 6 x 7 x 8 = n - 1 = prime number
or
x ? 5 x 6 x 7 x 8 = n - 1 = prime number

I can not test the true mechanism , but i think ( you see 4 x 5 x 6 , 3 times , and the number moltiplication 3 always after a series of numbers ) , i think that ,in this mechanism there is peralps hide one algorithm particular for to find a prime numbers.
I see 4*5*6 4 times. I'm still missing something or I don't see why this should always produce primes in fact I can telll you for ? not more than 8 the first multiplication you suggest never gives a prime:

Code:
(13:37) gp > %32*2 * 4 * 5 * 6 * 3 * 4 * 5 * 6 * 3 * 6 * 7 * 8
%39 = 265410020093460480000000
(14:03) gp > for(x=1,8,print(isprime(x*%39-1)))
0
0
0
0
0
0
0
0
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Old 2015-11-24, 18:14   #8
Ale
 
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or this

3047495270400000 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 x 8 = n - 1 = prime number
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Old 2015-11-24, 18:18   #9
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Quote:
Originally Posted by Ale View Post
or this

3047495270400000 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 x 8 = n - 1 = prime number
No it isn't.

Code:
(14:04) gp > 3047495270400000*3*4*5*6*3*5*6*7*8
%41 = 5529375418613760000000
(14:16) gp > isprime(%-1)
%42 = 0
(14:16) gp > factor(%41-1)
%43 =
[    580824613 1]

[9519871050323 1]

Last fiddled with by science_man_88 on 2015-11-24 at 18:19
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Old 2015-11-24, 23:48   #10
ewmayer
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Quote:
Originally Posted by Ale View Post
now 8 is:

3 x 3 x 2 x 4 x 3 x 2 x 3 x 4 x 5 x 3 x 2 x 4 x 3 x 4 x 5 x 6 x 3 x 4 x 5 x 3 x 4 x 5 x 6 x 3 x 5 x 6 x 7 x3 x 2 x 4 x 5 x 6 x 3 x 4 x 5 x 6 x 3 x ? 6 x 7 x 8 = n - 1 = prime number
or
x ? 5 x 6 x 7 x 8 = n - 1 = prime number

I can not test the true mechanism , but i think ( you see 4 x 5 x 6 , 3 times , and the number moltiplication 3 always after a series of numbers ) , i think that ,in this mechanism there is peralps hide one algorithm particular for to find a prime numbers.
I assume the '?' in there is a stray character - deleting it and replacing the 'x' with '*', PARI (which is a freely downloadable for you as it was for me, hint, hint) shows this number is composite:

? factor(3*3*2*4*3*2*3*4*5*3*2*4*3*4*5*6*3*4*5*3*4*5*6*3*5*6*7*3*2*4*5*6*3*4*5*6*3*6*7*8-1)
%2 =
[71 1]

[11214507891272978028169 1]

And you still have not given an actual *algorithm* for how you generate these small-number product sequences. Please do so - it should only require very rudimentary English. Do it in Italian and then post it here, if you prefer - I'm sure one of our Italian-speaking regular readers could translate it.

If by '?' you mean 'I am not sure here', then in fact you have no algorithm, just a vague supposition - in that case, download PARI, learn its basic operations (*,+,-, isprime and factor are the main operators and functions you need), and see if you can work out an actual *algorithm* which generates more than 3 or 4 primes in succession.

Last fiddled with by ewmayer on 2015-11-24 at 23:49
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Old 2015-11-25, 05:12   #11
LaurV
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Re-arranging those small numbers, you only have a product of small primorials, n# multiplied by m# etc, and subtract 1.
For small n, m, etc, this has higher chance to generate a prime, because n#-1 does not have prime factors under n.
As n grows, your chances to find a prime by this method are as much as picking a random odd number and test it if it is prime or not.
Therefore is a fallacy.

As suggested above, if you have and algorithm, post it in Italian and I can handle the translation (I am Romanian).

Last fiddled with by LaurV on 2015-11-25 at 05:14
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