is there a prime equal to its position in the sequence of primes?

if i understand what youre trying to say, no because any prime is strictly larger than its position # since most numbers arent primes

i.e. p_1 = 2 > 1
p_2 = 3 > 2
p_3 = 5 > 3

>>8572815

Kek, OP did not think 5 seconds before posting.

>>8572813
Really dude? How in the hell would that even work?

>>8572815
Even if every number after 2 was prime, it would still be impossible as the position of prime p would be p-1

Now let's prove the conjecture.

Assume for induction p_k > k for some k

p_1 = 2 > 1 is the base case

p_n+1 > p_n

p_k+1 > p_k > k

Since all primes are by definition integers and k is an integer

p_k+1 > p_k >= k+1

p_k+1 >= k+1

So by induction p_n > n

>>8572893
Woops last line should be p_k+1 > k+1