Just want to share an Observation on Twin Primes

[NaveedBajwah]

Hello,
I want to share a little observation on the twin primes.
Statement: "Consider a twin prime (p1, p2), such that (p1=x+y) & (x and y are positive integers) & (p1>3)
There exists some decomposition of p1=x+y such that x and y written together form a new first digit of twin pair p1' (p1'>p1)".
Example: "Consider (5,7) a twin prime pair. Now if we decompose 5 such that 5=4+1, then 41 is new twin prime pair (first digit)"
Its kind of a foolish observation but the problem is that the phenomenon is occuring upto a billion (and probably more than that). I just want to know if its some part of a conjecture or result or its a whole new problem. I suspect its some result of an already existing conjecture but i want to know the east or west of it.

[HallsofIvy]

I don't know what you mean by "new first digit". In what sense is 41 a "digit"?