Prime numbers

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Pigeon
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Prime numbers

Post by Pigeon » Sun May 04, 2014 10:54 pm

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

Goldbach's conjecture (that every even integer greater than 2 can be expressed as the sum of two primes)

Twin prime conjecture (that there are infinitely many pairs of primes whose difference is 2).

The first 168 prime numbers (all the prime numbers less than 1000) are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
(sequence A000040 in OEIS).


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Pigeon
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Re: Prime numbers

Post by Pigeon » Sun May 04, 2014 10:58 pm

3, 5
5, 7
17, 19
29, 31
41, 43
59, 61
71, 73
101, 103
107, 109
137. 139
191, 193
197, 199
227, 229
281, 283
311, 313
...

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Pigeon
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Re: Prime numbers

Post by Pigeon » Mon May 05, 2014 1:53 am

I wrote a program to do this.

It uses the Sieve of Eratosthenes to get the primes less than 1000 which is 168.

Then it found 35 sets of twin primes.

In case you are wondering:

303 primes and 61 twins for primes up to 2000

61> 1997 1999

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Royal
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Re: Prime numbers

Post by Royal » Tue May 06, 2014 3:36 am

What are the practical applications of Prime numbers?

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Pigeon
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Re: Prime numbers

Post by Pigeon » Tue May 06, 2014 11:04 am

Public key encryption

For a long time, number theory in general, and the study of prime numbers in particular, was seen as the canonical example of pure mathematics, with no applications outside of the self-interest of studying the topic. In particular, number theorists such as British mathematician G. H. Hardy prided themselves on doing work that had absolutely no military significance.

However, this vision was shattered in the 1970s, when it was publicly announced that prime numbers could be used as the basis for the creation of public key cryptography algorithms. Prime numbers are also used for hash tables and pseudorandom number generators.

This is interesting...

Prime numbers in nature

Inevitably, some of the numbers that occur in nature are prime. There are, however, relatively few examples of numbers that appear in nature because they are prime.

One example of the use of prime numbers in nature is as an evolutionary strategy used by cicadas of the genus Magicicada.[40] These insects spend most of their lives as grubs underground. They only pupate and then emerge from their burrows after 7, 13 or 17 years, at which point they fly about, breed, and then die after a few weeks at most. The logic for this is believed to be that the prime number intervals between emergences make it very difficult for predators to evolve that could specialize as predators on Magicicadas


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Pigeon
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Re: Prime numbers

Post by Pigeon » Tue May 06, 2014 11:27 am

Ran across this comment

Prime number are used in developing machine tools. Utilizing primes you can avoid setting up harmonics which "eat" your very expensive tools. Tools chatter, (bounce up and down), as they are being used. Allowing those vibrations to propagate intensifying the chatter and the wear.

You ever wonder how the metal racks in a microwave get designed? Again they use primes to assure that there are no harmonic possibilities, and you don't get the light show you would on an older microwave.

Link


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Kat
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Re: Prime numbers

Post by Kat » Tue May 06, 2014 11:46 am

I am a prime number devotee. Therefore I have posted the 7th post on this salient topic.
If I could get any animal it would be a dolphin. I want one bad. Me and my mom went swimming with dolphins. I was like, 'How do we get one of those?' and she was like, 'You can't get a dolphin. What are you gonna do, put it in your pool?' Miley Cyrus

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Royal
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Re: Prime numbers

Post by Royal » Wed May 07, 2014 3:31 am

Pigeon wrote:Ran across this comment

Prime number are used in developing machine tools. Utilizing primes you can avoid setting up harmonics which "eat" your very expensive tools. Tools chatter, (bounce up and down), as they are being used. Allowing those vibrations to propagate intensifying the chatter and the wear.

You ever wonder how the metal racks in a microwave get designed? Again they use primes to assure that there are no harmonic possibilities, and you don't get the light show you would on an older microwave.

Link

I like this one.

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Pigeon
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Re: Prime numbers

Post by Pigeon » Wed May 07, 2014 7:05 pm

Post 9, the square of a prime.

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Royal
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Re: Prime numbers

Post by Royal » Sun May 11, 2014 12:06 am

The 10th, 5/10 - Not a Prime.

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