News that researchers in the United States have discovered a new highest prime number has both mathematical and religious significance.
The number - discovered at the University of California at Los Angeles - is the first to be discovered with 10 million decimal digits. The new Mersenne prime (after the 17th century French mathematician) is in the form 2P - 1 (where P is a power) and has P = 43,112,609.
As well as having application in encryption codes and credit card processing, prime numbers also have theological significance.
Some systems of atheist thought (and some agnostics) have argued that it is impossible to make a finite statement about an infinite subject - such as "god".
Euclid's proof that there is no highest prime number, however, is an example of such a finite statement being made about an infinite subject - in this case numbers.
Although Euclid's proof - which has stood the test of time since around 300 BC - covers numbers not divinity and although it does not prove the existence of God, it does prove that finite, human language is capable of describing limitless concepts. In this sense, it undermines the claim that nothing meaningful can be said about God because of the limitations of language.
In case you hadn't recited it for a while, Euclid's proof is as follows, courtesy of the University of York:
The number - discovered at the University of California at Los Angeles - is the first to be discovered with 10 million decimal digits. The new Mersenne prime (after the 17th century French mathematician) is in the form 2P - 1 (where P is a power) and has P = 43,112,609.
As well as having application in encryption codes and credit card processing, prime numbers also have theological significance.
Some systems of atheist thought (and some agnostics) have argued that it is impossible to make a finite statement about an infinite subject - such as "god".
Euclid's proof that there is no highest prime number, however, is an example of such a finite statement being made about an infinite subject - in this case numbers.
Although Euclid's proof - which has stood the test of time since around 300 BC - covers numbers not divinity and although it does not prove the existence of God, it does prove that finite, human language is capable of describing limitless concepts. In this sense, it undermines the claim that nothing meaningful can be said about God because of the limitations of language.
In case you hadn't recited it for a while, Euclid's proof is as follows, courtesy of the University of York:
- Assume there are a finite number, n, of primes, the largest being pn.
- Consider the number that is the product of these, plus one: N = p1...pn+1.
- By construction, N is not divisible by any of the pi.
- Hence it is either prime itself, or divisible by another prime greater than pn, contradicting the assumption.
For example:
- 2 + 1 = 3, is prime
- 2*3 + 1 = 7, is prime
- 2*3*5 + 1 = 31, is prime
- 2*3*5*7 + 1 = 211, is prime
- 2*3*5*7*11 + 1 = 2311, is prime
- 2*3*5*7*11*13 + 1 = 30031 = 59*509
- 2*3*5*7*11*13*17 + 1 = 510511 = 19*97*277
- 2*3*5*7*11*13*17*19 + 1 = 9699691 = 347*27953
- 2*3*5*7*11*13*17*19*23 + 1 = 223092871 = 317*703763
- 2*3*5*7*11*13*17*19*23*29 + 1 = 6469693231 = 331*571*34231
- 2*3*5*7*11*13*17*19*23*29*31 + 1 = 200560490131, is prime
- 2*3*5*7*11*13*17*19*23*29*31*37 + 1 = 7420738134811 = 181*60611*676421
- etc.
Alternatively, to get started, the following video shows how to begin the process of manually calculating prime numbers from 1 to 100.
And finally, UCLA's discovery was the result of its participation in the Great Internet Mersenne Prime Seach - an online project which allows individual PC owners to contribute some of their processing capacity in order to passively calculate further larger prime numbers.
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