I also downloaded Python (ver. 2.4.2 window),
in command mode
when I typed
prime = (28433 * (2 ** 7830457) + 1)
it finished in about one second. I timed it using handheld stopwatch.

very fast for
prime = (28433 * (4 ** 7830457) + 1)
prime = (28433 * (8 ** 7830457) + 1)
prime = (28433 * (16 ** 7830457) + 1)

but it take forever to compute
prime = (28433 * (3 ** 7830457) + 1)


apparently, there is some clever method to calculate 2&^


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