Re: [PrimeNumbers] A Prime Number Case to Consider
- Bill Sindelar wrote:
> Consider these 4 prime numbers namely, A= 1049681, B= 1049683,Consider these 8 consecutive primes:
> C= 1049861, D=1049863. Some interesting facts are: One, A and B
> are twins. C and D are twins and the pair (A, B) and the pair
> (C, D) are consecutive twin pairs. Two, the digits that define A
> are the same as the digits that define C and they sum to the twin
> 29. The digits that define B are the same as the digits that
> define D and they sum to the twin 31.
1475408862860716126025520041510000 + n,
for n = 0121, 0123, 0211, 0213, 1021, 1023, 1201, 1203
They form four consecutive twin prime pairs where the lower twin
members (n = 0121, 0211, 1021, 1201) contain the same digits,
and so do the upper members (n = 0123, 0213, 1023, 1203).
The smallest possible width in such a constellation is 1082 like
in the above 84-digit example. The requirement for 1075 composite
numbers would make it harder to find a small example.
Jens Kruse Andersen