Friday, May 18, 2012

Sum Of Prime Number Digits To One Digit


Prime numbers are numbers which can only be divided by themselves and the number ( 1 ). The first five ( 5 ) single digit prime numbers are ( 1, 2, 3, 5, 7 ). The total of the single digit prime number digit's are ( 1 + 2 + 3 + 5 + 7 = 18 ). For two digit prime numbers ( 11, 13, 17, 19 ) or one's over two digits like ( 137) you will find their digits will add to one of ( 1, 2, 4, 5, 7, 8 ). The sum of these digits are ( 1 + 2 + 4 + 5 + 7 + 8 = 27 ). You will notice for prime numbers over one ( 1 ) digit, that none of the single prime number digits total 3 or a multiple of 3. For the first five ( 5 ) single digit prime numbers ( 1, 2, 3, 5, 7 ), there is one even prime number ( 2 ) and ( 4 ) odd prime numbers. Since the total of the digits of single digit prime numbers are the same, you have more odd totals ( 4 ) than even ( 1 ) which is for the prime number 2. For prime numbers greater than one digit you have ( 3) even totals ( 2, 4, 8 ) and ( 4 ) odd ( 1, 3, 5, 7 ). Two researchers from the Institute of Mathématics of Luminy have recently made an important breakthrough regarding a conjecture formulated in 1968 by the Russian mathematician Alexandre Gelfond concerning the sum of digits of prime numbers. In particular, they have demonstrated that, on average, there are as many prime numbers for which the sum of digits is even as prime numbers for which it is odd. Since prime numbers may have different one digit totals that aren't in sequence, even though the prime numbers are linear they are probably correct on average ( 3 even one digit totals Р2, 4 8 ), ( 4 odd one digit totals Р1, 3, 5, 7 ).

Here's some more interesting stuff:
  1. Prime numbers, if they are prime numbers, have the numbers 1, 3, 7, 9 in column 0 ( farthest right column ).
  2. Except for prime number ( 3 ) , if the sum of the digits of any number ending in 1, 3, 7, 9, total a multiple of 3, ( for instance total 6, 9, 12, etc. ) it isn’t a prime number. If a number ending in 1, 3, 7, 9 in column zero (0), isn’t a prime number it can usually be evenly divided by a number with 1, 3, 7, 9 in column (0).
  3. The sum of the one digit prime's digits ( 1, 2, 3, 5, 7 ) total 18 ( 1 + 2 + 3 + 5 + 7 = 18 ). The sum of the more than one digit prime's digits ( 1, 2, 4, 5, 7, 8 ) total 27 ( 1 + 2 + 4 +5 + 7 + 8 = 27 ). 9 divides evenly into 18 ( 18 / 9 = 2 ) and evenly into 27 ( 27 / 9 = 3 ). 9 is the only number that isn't a prime digit that appears in column 0 ( far right column ) of a prime number.

No comments: