Do I need a supercomputer?

Number Theory Level 2

GIMPS has discovered the largest known prime number, 2 77232917 − 1 2^{77232917} - 1 , having over 23 million digits!

What is the remainder when this large number is divided by 59?

1 3 5 7 9

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Ryoha Mitsuya
Jan 13, 2018

Using fermat’s theorem, 2 77232916 ≡ 1 ( m o d 59 ) \displaystyle 2^{77232916} \equiv 1 \pmod{59} . So 2 77232917 − 1 ≡ 1 ( m o d 59 ) \displaystyle 2^{77232917} -1 \equiv 1\pmod{59} → 1 \displaystyle \rightarrow\boxed{1}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Giorgos K.
Jan 4, 2018

You don't need a supercomputer... Just Mathematica:
Mod[2^77232917-1,59]
1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

But I already bought one just to solve this problem! Sigh...

Pi Han Goh - 3 years, 5 months ago

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