Answer
You asked one like this before. Each time we muliply by 99,193, the one's digit gets multiplied by 3, so it goes (starting from the 1st power) 3,9,7,1,3,9,7,1,3,9,7,1... Since 4131/4 has a remainder of 3, the result ends with 7.
Now, find the largest prime number there is, or prove that they go on forever.
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