If there are an even number of 4's, then it is a palindrome with an even number of digits, so it is divisible by 11. If the number of 4's is divisible by 3, say 3n, then the sum of the digits is 12n+18, which is divisible by 3, so the number is divisible by 3. The only other possible numbers of 4's are 6n+1 and 6n+5. However, if the number of 4's is of the form 6n+1, then it is divisible by 13, and if the number of 4's is of the form 6n+5, then it is divisible by 7. Therefore, no number in the sequence 949, 9449, 94449... is prime.

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