sauravshakya
t(1)=2
t(2)=3
t(3)=t(1)*t(2)+1
t(4)=t(1)*t(2)*t(3)+1
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.
.
t(n)=t(1)*t(2)*t(3)*...*t(n1)+1
PROVE or DISPROVE that t(n) will surely be PRIME



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TuringTest
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This sounds like a very hard problem.

estudier
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Maybe not....

sauravshakya
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I dont know..... But I think it will not be surely prime.

estudier
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If not, we just need a counterexample.

TuringTest
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I doubt it is all primes as well.

UnkleRhaukus
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remainder is gonna be one

klimenkov
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Looks like an Euclid proof of the infinite number of prime numbers.

estudier
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Euclid never said there was an infinity of primes (didn't believe in infinity)

swissgirl
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t(5)=2*3*7*43+1=1807
1807/13=139

estudier
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Euclid said that you could always construct another one out of a supposedly complete list.

UnkleRhaukus
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that dosent make sense


estudier
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True but he never said anything about infinity (Greeks weren't too keen on that idea)

klimenkov
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You deepened into the history. But I spoke about the method.

estudier
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The method, I agree, is very like the question.....

estudier
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P_n = p1p2p3....+1

UnkleRhaukus
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estudier
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The "infinitely many" part got added later.....

estudier
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Personally, I like "you can always get another one" better....

estudier
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"Construct another one"

UnkleRhaukus
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do you mean induction

estudier
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No, it is an explicit construction...

estudier
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You give me a list of primes and say "That's all there are"
And I give you another one not in the list...