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Calculus/Prime numbers

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Expert: - 5/24/2005


Question
How many prime numbers between one and one million become perfect squares when 1 is added to them

There are 78497 prime numbers between one and one million

Answer
BTW: there are 78498 primes between 1 and 1000000...

Hello Maxine,

Only One!  Namely, 3 (3+1=4=2^2).

Proof:
Let p=a prime number
==> p+1=n^2 ==> p=n^2-1=(n+1)(n-1)
but if p is prime, then its only factors
are 1 and iteself...thus, n-1=1 ==> n=2
==> p=3

OK?

Abe

Calculus

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Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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