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Some Large Primes and Amicable Numbers

Some Large Primes and Amicable Numbers

Some new large primes of the form $3 \cdot {2^n} - 1$ and $9 \cdot {2^n} - 1$, related to amicable numbers, are given. Two new large amicable number pairs are found by the method of so-called "Thabit rules".