Is 1000000000000066600000000000001 prime number

This specific number (1 followed by many zeros with 666 in the middle) is almost certainly not prime, though definitively proving primality for numbers this large requires computational verification. Numbers with special patterns like this are often composite (non-prime) because their structure makes them vulnerable to certain factorization methods.

For context, determining primality of such large numbers is computationally intensive. The number you've written has 31 digits, which is large but still manageable for modern primality testing algorithms like Miller-Rabin. However, numbers with obvious patterns or specific structures often have mathematical properties that make them factorable. The placement of 666 in the middle creates a particular structure that cryptographers and number theorists could analyze, but without actually running primality tests, I cannot definitively say whether it's prime. If you're genuinely interested in this number's primality, computational tools like Mathematica, PARI/GP, or online primality testers could verify it. That said, randomly chosen large numbers are much less likely to be prime than small numbers, and patterned numbers like this one are even less likely to be prime due to their internal structure potentially revealing factors.