I'm taking that to mean the earliest string of 7 digits in pi which are a Prime number. There's one just three decimal places in: 3.141592653, and it actually overlaps with the next one, 6535897.
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There is no such thing as a "prime number of pi". The lowest 7-digit prime number is 1000003 (according to Wolfram Alpha); given that the digits of pi seem to be sort of randomly distributed, it is almost certain that this sequence of digits appears somewhere in the decimal expansion of pi.
pi is an irrational (transcendental) number and so has no prime factors. So there cannot be a lowest 7-digit prime.
pi is just one number. The 324th digit of pi is 1.
3.141592653589793238462643
the first 35 digits of pi is... 3.14159265358979323846264338327950288
Pi is an irrational number, meaning it has an infinite number of decimal places that do not repeat. Therefore, there is no "last digit" of pi. However, for practical purposes, the last digit commonly used is 3, as it is the third decimal place in the number 3.14159.
There is no last digit of pi. It is possible to calculate the digits of pi an infinite number of times. The one millionth number is 5.