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Largest Prime Number for 2016


As the new year approaches, you may be (or not be) interested to learn that the largest known prime number is 274,207,281– 1.

This number is an incredible 22 million digits long and 5 million digits longer than the second largest prime number. Hang on to your primes you might ask, “Why are prime numbers important? Are they of any practical use in real life?

Barak Shoshany, Graduate Student at Perimeter Institute for Theoretical Physics, helps answer your question. “The most notable practical use of prime numbers is in cryptography. Many popular algorithms used in public-key cryptography, which has numerous and extremely important security applications (your computer is probably using several of these algorithms at this very moment), are based on the fact that integer factorization is a “very hard” problem.

What this means is that the time required to factorize integers into their prime factors grows (roughly) exponentially with the number of bits in the integer. So if the encryption uses very large integers, it would take an unrealistic amount of time to “crack” it.

If (or when) quantum computers become a reality, they would have the potential to make all of these algorithms obsolete, since there are quantum algorithms (in particular Shor’s algorithm) that can factor arbitrarily large integers much faster than any known classical algorithm. This has led to the very important field of post-quantum cryptography.”

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10 x 9 x 8 + (7 + 6) x 5 x 4 x (3 + 2) x 1 = 2020

NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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