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Old 2022-11-15, 00:42   #1
Harklo73
 
Jan 2022

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Smile new formula for prime numbers?

Hello everyone,
I found an interesting formula in a book.
It is the formula n^2-9n+61.
It produces a lot of prime numbers.
Currently i am checking range 0k-100k
Found a lot of primes!
Hope to hear more about this.
Best Regards.
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Old 2022-11-15, 04:46   #2
LaurV
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Please post here the largest prime you found.
Only one, please. Chose the largest, and tell us how you found it.
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Old 2022-11-15, 06:09   #3
Batalov
 
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Quote:
Originally Posted by Harklo73 View Post
new formula for prime numbers?
Please explain what do you think the word "formula" means.
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Old 2022-11-15, 13:14   #4
Harklo73
 
Jan 2022

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Default largest prime number i found so far with n^2-9n+61

This is the largest prime number i found so far: (2^27450)^2-(9*(2^27450))+61
Currently i am checking k until 30k.
I found the prime with openPFGW.
Best Regards.
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Old 2022-11-15, 13:25   #5
Harklo73
 
Jan 2022

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Smile its not a formula you are right

You are right, it is not a formula but a sequence.
Best Regards.
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Old 2022-11-15, 14:28   #6
Dr Sardonicus
 
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It's certainly not new.

n^2 - 9*n + 61 = (n-4)^2 - (n-4) + 41

is merely a shift of Euler's "prime-generating polynomial" n^2 - n + 41.
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Old 2022-11-16, 17:27   #7
bhelmes
 
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Quote:
Originally Posted by Harklo73 View Post
You are right, it is not a formula but a sequence.
Best Regards.
The polynomial f(n)=n²-n+41 has the discriminant b²-4c=1-4*41=-163,

For this special case I recommend a sieve procedure similar like the sieve of Eratosthenes:
http://devalco.de/basic_polynomials/...?a=1&b=-1&c=41

For a more general point of view take:
http://devalco.de/poly_sec.php

If you want to speed up the finding for primes for f(n)=n²-n+41 I suggest a quadratic presieve
and then the check for primes.

Have a lot of fun with the theory and with the programming.
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Old 2022-11-17, 14:34   #8
Harklo73
 
Jan 2022

1216 Posts
Thumbs up sequence

Thank you!
I will start with it immediately.
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Old 2022-11-19, 19:35   #9
Harklo73
 
Jan 2022

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Default Siever

Hello everyone,
I made a siever for n^2-n+41.
Its written in Python so its very slow.
I am working on a c or freebasic version now.
I keep you updated.
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