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Old 2013-09-18, 11:44   #3
gd_barnes
 
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May 2007
Kansas; USA

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Quote:
Can we be certain that all theorized PalPrimes of this nature are actually Prime.
To clarify further:

At this time, we can be certain that only 2 of them are prime. The only known primes in this series are for n=1 and 2, i.e. 10^1+1 and 10^2+1 or simply 11 and 101. All n's have been tested up to n=2^24-1.

In a synopsis, this means that all 10^n+1 where n<2^24 have effectively been tested for primality, which only required that 24 tests be run, i.e. n=2^0, 2^1, 2^2, 2^3, etc. up to 2^23.

It is unlikely that there are any more primes in this series but there is no way to prove that with current technology and knowledge.

Last fiddled with by gd_barnes on 2013-09-18 at 21:32
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