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Prime or composite?

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How to determine if the following number is prime or composite? [7^79*11^61 *3^103] + 2
Thank you.

Guest Jul 20, 2017
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[7^79*11^61 *3^103] + 2 =269890 869144 776692 058199 465698 454668 923873 714985 443368 694900 724411 839791 502548 735241 697126 029468 101948 846438 577644 440037 966181 262067 823221 151182 817586 921742 833615 938280 212191 361073 (180 digits)

Using primality test of Rabin-Miller, it clearly shows that it is a composite number. In fact, it has 2 small prime factors and a large composite factor as follows:

= 2069 × 15173 × 8597 184428 611336 749352 233774 700808 303596 242523 770342 631366 435208 398621 368320 802072 188948 935535 025026 452492 755859 206165 959119 443397 979081 127426 300304 011750 886309 743439 430729 (172 digits).

Guest Jul 20, 2017

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