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# Prime factors- I'm not sure how to do this.

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What is the product of the two smallest prime factors of 2^{1024} - 1?

I don't know where to start at all on this. It's in the form of a Mersenne prime but I don't know how that would help. I also do not know how to find the prime factors.

Jul 9, 2020
edited by gwenspooner85  Jul 9, 2020

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The equation isn't prime...

It's in the form of a^2-b^2

IT CANNOT BE PRIME!

It is the factors of (a-b) x (a+b).

Whatever...

Factoring the equation, we get the following factors:

(2 ^ 1024) - 1=(2^512 - 1) x (2^512 + 1)

Now you may see something that you can do.

Factor.

We can factor this equation for a long time until you get:

(2 - 1) x (2 + 1) .

Yay!

Jul 9, 2020
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It factors into the following primes:

= 3 × 5 × 17 × 257 × 641 × 65537 × 274177 × 2 424833 × 6 700417 × 67 280421 310721 × 1238 926361 552897 × 59649 589127 497217 × 5704 689200 685129 054721 × 93 461639 715357 977769 163558 199606 896584 051237 541638 188580 280321 (62 digits) × 5529 373746 539492 451469 451709 955220 061537 996975 706118 061624 681552 800446 063738 635599 565773 930892 108210 210778 168305 399196 915314 944498 011438 291393 118209 (148 digits)