The Hunt For The First Billion Digit Prime Number

Jan 2016
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Late last year, a researcher by the name of Patrick Laroche discovered the largest prime number that we know of, a monster of a number with 24,862,048 digits. But there is no largest prime number; there exists an infinite number of prime numbers, a fact we have known since Euclid proved it with a very elegant proof by contradiction back around 300 BC. So the hunt is on for ever larger prime numbers. There is a prize of $150,000 waiting for the first person to discover a prime number with more than 100 million digits......and a bigger prize of $250,000 waiting for the discoverer of the first billion-digit prime number. This and much more is discussed in this fascinating article, "The Call of the Primes", in the latest issue of New Scientist:

Inside the race to find the first billion-digit prime number

An interesting side-bar to the main article takes note that we have now calculated the value of the irrational constant pi out to 31.4 Trillion digits, a feat done by a Google developer from Japan, Emma Haruka Iwao.

And another interesting historical note: In 1588, the Italian mathematician Pietro Cataldi was able to prove that the number 524,287 is a prime number, and that would remain the largest known prime number for nearly two centuries!

Boy, we've come a long ways since then!
 
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And what value does this have in the real world? I'm not being cynical; just asking as I don't know.
 
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Jan 2016
57,388
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And what value does this have in the real world? I'm not being cynical; just asking as I don't know.
The difficulty of factoring large numbers, especially when a number is the product of two large prime numbers, is the entire basis of RSA Encryption, which is used worldwide for secure data transmission. Hence finding new very large prime numbers strengthens the security of data transmission:

RSA (cryptosystem) - Wikipedia

Up until about the mid-1970's, the subfield of mathematics known as number theory was considered to be 'recreational mathematics', with little in the way of practical applications. But suddenly in the mid-1970's, the U.S. Government began stamping "Top Secret: Highly Classified" on papers in this field! It changed almost literally overnight from being an area of study with little practical application, to being the basis of our most secret codes.

Factoring large numbers can also be a way of 'testing' supercomputers-----to see how fast they can do it.
 

Ian Jeffrey

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Up until about the mid-1970's, the subfield of mathematics known as number theory was considered to be 'recreational mathematics', with little in the way of practical applications. But suddenly in the mid-1970's, the U.S. Government began stamping "Top Secret: Highly Classified" on papers in this field! It changed almost literally overnight from being an area of study with little practical application, to being the basis of our most secret codes.
That is awesome. Kind of like when the electron was discovered.

 
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CtC

Mar 2019
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The difficulty of factoring large numbers, especially when a number is the product of two large prime numbers, is the entire basis of RSA Encryption, which is used worldwide for secure data transmission. Hence finding new very large prime numbers strengthens the security of data transmission:

RSA (cryptosystem) - Wikipedia

Up until about the mid-1970's, the subfield of mathematics known as number theory was considered to be 'recreational mathematics', with little in the way of practical applications. But suddenly in the mid-1970's, the U.S. Government began stamping "Top Secret: Highly Classified" on papers in this field! It changed almost literally overnight from being an area of study with little practical application, to being the basis of our most secret codes.

Factoring large numbers can also be a way of 'testing' supercomputers-----to see how fast they can do it.
Yes. Program a computer with a high capacity to LOOK for non-Divisive numbers right up the scale.
 
Jan 2016
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54,207
Colorado
Yes. Program a computer with a high capacity to LOOK for non-Divisive numbers right up the scale.
The method you are suggesting for finding primes is very old, and is known as the Sieve of Eratosthenes. However, it is a terribly inefficient way to go about trying to factor a large number, and we have much more sophisticated algorithms today. Still, factoring really large numbers is HARD. And probably will remain that way until we have full-fledged quantum computers. That may happen in a decade or two. When it does, all our current methods of encryption will fail immediately.
 
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