Fun With Math 10 Mystery Cache
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The final cache in the 'Fun With Math' series explores the world
of Mersenne primes.
FTF Honors to:
WakeboardLanier
Mersenne primes are prime numbers which can be expressed as:
Named for Marin Mersenne, a French monk in the 17th century, the
first 4 Mersenne primes ( M2=3, M3=7,
M5=31, M7=127) were discovered before 250 BC.
It would take almost 1800 years before the next 4 (8191, 131071,
524287, and 2147483647) were discovered. The largest known Mersenne
prime (243,112,609 - 1) contains over 12 million digits
and is also the largest known prime number. Many fundamental
questions about Mersenne primes remain unresolved.
Note that p is a prime number for each of the 1st 4 Mersenne primes
(M2, M3, M5, M7). It
would seem that this pattern would continue. It can be
mathematically proven that if p is composite (non-prime) then
(2p - 1) will be composite. One could conjecture that if
p is prime, then (2p -1) will also be prime and thus a
Mersenne prime.
Your task is to find the lowest prime number that serves as a
counterexample to this conjecture. You are to find the lowest prime
number p so that (2p -1) = N is not prime. Show that it
is not prime by finding N's prime factors A & B. Use these
numbers to compute the coordinates of the cache at:
N 34 25.X
W 083 52.0Y
Where:
A < B
X = 34*A + 21
Y = B - 42
Additional Hints
(Decrypt)
Na nzzb pna va gur jbbqf!
Nf nyjnlf, rznvy zr vs lbh jnag gb purpx pbbeqvangrf orsber tbvat bhg va gur svryq.
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