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MultiplicativeOrder[37, 1000]
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MultiplicativeOrder[10^100 + 1, 7919] (*10^3th prime number Prime[1000]*)
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MultiplicativeOrder[10^1000 + 1, 15485863] (*10^6th prime number*)
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MultiplicativeOrder[10^10000 - 1, 22801763489] (*10^9th prime number*)
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MultiplicativeOrder[13, 1 + 10^80]
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MultiplicativeOrder[11, 1 + 10^100]
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