As of datenum 738289, three of the twenty largest known prime numbers are Proth primes, prime numbers of the form k 2^m+1 with k <= 2^m. For example, taking k = 1 and m = 1 gives 3, the first Proth prime, and taking k = 3 and m = 5 gives 97, the sixth Proth prime. The number 199 is prime but not a Proth prime because k = 99 > 2^m = 2. The number 49 is a Proth number (k = 3, m = 4) but not prime.
Write a function to list the Proth primes between two limits a and b. Also provide the values of k and m.
Optional: Values of k for which no values of k 2^m + 1 are prime are called Sierpinski numbers. Show that 78,557 is the smallest Sierpinski number. For more, see this page.
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