Fails for 11^13 + 11 + 13
Using: Big Integer Calculator - Arbitrary Precision Arithmetic
11^13 + 11 +13 = 34522712143931 + 24
= 34522712143955 is not a prime! It is 5 * 6904542428791 [A Primality Test]
This is quite common - that something may be prime but only for small numbers.
A classical example: Fermat number 2^2^n +1
F_n is prime for n = 0, 1, 2, 3 and 4: 3, 5, 17, 257, 65537
Fermat conjectured that they are all prime.
But some time later, Euler proved that the next number, 4294967297 = 641 × 6,700,417 - see Fermat prime (mathematics)
All of the Fermat numbers from then on up as far as we have gone are composite.
Yet - nobody knows if there is a larger Fermat prime or not :).
Seems that probably they are all composite - perhaps - but nobody can say that for sure.
Prime numbers are gnarly :)
Using: Big Integer Calculator - Arbitrary Precision Arithmetic
11^13 + 11 +13 = 34522712143931 + 24
= 34522712143955 is not a prime! It is 5 * 6904542428791 [A Primality Test]
This is quite common - that something may be prime but only for small numbers.
A classical example: Fermat number 2^2^n +1
F_n is prime for n = 0, 1, 2, 3 and 4: 3, 5, 17, 257, 65537
Fermat conjectured that they are all prime.
But some time later, Euler proved that the next number, 4294967297 = 641 × 6,700,417 - see Fermat prime (mathematics)
All of the Fermat numbers from then on up as far as we have gone are composite.
Yet - nobody knows if there is a larger Fermat prime or not :).
Seems that probably they are all composite - perhaps - but nobody can say that for sure.
Prime numbers are gnarly :)
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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