Welcome to the ToeQuest.
Page 1 of 4 1234 LastLast
Results 1 to 10 of 31
  1. #1
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Fundamental theorem of arithmetic

    It was Euclid in 300 B.C. who first attempted a theory of numbers, the study of the properties of whole numbers and ratios of whole numbers. This theory can only be found in Books VII, VIII, and IX of his Elements. In them Euclid represents numbers as line segments and the product of two numbers as rectangle. These geometric representations were supported by verbal arguments and proofs in contrast to modern usage of symbols. He did prove the non-existence of a largest prime number by reduction ad absurdum that is based on the false assumption that there is a largest prime.

    To this day, the theory of prime numbers remains unsolved even though many conjectures exist. The one listed in the Millennium Problems is known as the Riemann Hypothesis with a prize tag of $1 Million for the person or persons proving it correctly. Analogous to Goldbach conjecture that every even whole number greater than 2 is the sum of two primes and even though it is not proved or disproved, the fundamental theorem of arithmetic was proved by basic axioms on whole numbers as from a unique factorization theorem of prime decomposition. Simply stated, it says that every composite number can be decomposed into at least two prime factors. For examples: 4=2x2, 9=3x3, 8=2x2x2, 15=3x5, and 12709189=3559x3571. In the science and technology of modern encryption the larger the prime factors are the more secure the coded signals become. In 1903, Frank Nelson Cole (1861-1926) showed that 2 raised to 67th power minus 1 is a composite number with two prime factors: 193707721 and 16183257287.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  2. #2
    Grandmaster
    Join Date
    Feb 2007
    Location
    United States
    Posts
    11,904
    Blog Entries
    28
    Thanks Given
    1,782
    Thanked 3,989x in 2,767 Posts
    Rep Power
    181

    Awards Showcase

    Re: Fundamental theorem of arithmetic

    Remember the guy who spent years on figuring pi to thousands of digits by using only a pencil, but then had to start all over because he make a mistake in position 712?

    Also, it is said that a quantum computer could unencrypt large primes and find the factors instantly.

    Also, I think numbers started out as having n number of line segments in each.

  3. #3
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: Fundamental theorem of arithmetic

    what we need to find out is what algorithm these claims are using.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  4. #4
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: Fundamental theorem of arithmetic

    When you add it all up my friend,what does it REALLY amount to!




    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

  5. #5
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: Fundamental theorem of arithmetic

    nothing short of infinity. By the way, the uses of prime factors are in enscription such as the security of all internet access.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  6. #6
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: Fundamental theorem of arithmetic

    Quote Originally Posted by AntonioLao View Post
    nothing short of infinity. By the way, the uses of prime factors are in enscription such as the security of all internet access.

    Anything shorter would not cut the mustard!




    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

  7. #7
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: Fundamental theorem of arithmetic

    Or the custard.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  8. #8
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: Fundamental theorem of arithmetic

    Quote Originally Posted by AntonioLao View Post
    Or the custard.

    Fancy me for omitting the custard,I;ll forget the rhubarb next!





    regards michael.
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

  9. #9
    Raider of the lost time
    Join Date
    Nov 2003
    Location
    United States
    Posts
    11,778
    Blog Entries
    10
    Thanks Given
    1,106
    Thanked 1,472x in 1,192 Posts
    Rep Power
    158

    Re: Fundamental theorem of arithmetic

    To exercise your memory is one way to memorize the first billion prime numbers.
    Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: a(tr(t)=c²

  10. #10
    Moderator
    Join Date
    Aug 2005
    Location
    United Kingdom
    Posts
    11,621
    Blog Entries
    5
    Thanks Given
    295
    Thanked 896x in 724 Posts
    Rep Power
    154

    Smile Re: Fundamental theorem of arithmetic

    Quote Originally Posted by AntonioLao View Post
    To exercise your memory is one way to memorize the first billion prime numbers.
    I will start on that first thing tomorrow.




    regards michael
    Humilty,coupled with boldness,surprises truth to
    reveal herself?

 

 
Page 1 of 4 1234 LastLast

Thread Information

Users Browsing this Thread

There are currently 1 users browsing this thread. (0 members and 1 guests)

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Back to top