Re:Another theme of concatenated integers.

>These integers concatenated --- >1,2,3,4,5,6,7,8,9,10,11..n
>at any point in their concatenation ever be a prime?
>I believe that they never will be prime!

>Not a proof but their sum at any point in the
>concatenation equals a triangle number and all
>triangle numbers except 3 are not prime.
>Ruling out all 0(mod 3) and 0(mod 5) and even ending
>integers the list of composites to check would be --


>1234567
>12345678910111213
>12345678910111213141516171819
>12345678910111213141516171819202122232425262728293031
>continuing with the concatenation the next ending integers would be --
>37,43,49,61,67,73,79,91..

>Also note that these composites end in an odd t(7),
>t(13),t(19),t(31) and t(37)that are triangle numbers
>that are not congruent to 0(mod 3) or 0(mod 5).

>t(7)=28,t(13)=91,t(19)=190,t(31)=496,t(37)=703,
>t(43)=946,t(49)=1225.. etc. All = (1) after casting
>9's

>Dan

Simplifying my discovery ---
I know ending integer 97 is a candidate because
t(97) =4753 ==1(mod 3) for entire concatenation.----
12345678910111213....97
101 is not because t(101) = 5151== 0(mod 3) for entire concatenation. --- 12345678910111213.....101

Doing this with no prior adding of digits or
dividing by 3.

Ending integers --
103 candidate
107 no
109 candidate
113 no
119 no
121 candidate
127 candidate
131 no
133 candidate
137 no
139 candidate
etc.
As an example-- given a 4 digit ending integer 2791
t(2791) = 3896236 == 1(mod 3) then take all concatenated
integers prior too 2791 --- 123456789101112.....2791
so this entire concatenation is not a 0(mod 3) integer
thus making it a candidate.

I hope this clarifies my discovery about this concatenation and the triangle number connection and most important, why none of these concatenations
can never be prime.

Thanks to all for your input.

Dan
.