The Default NTT Prime

A large power of two dividing $p-1$ is what guarantees a primitive $2^k$-th root of unity for every $k \le 23$, which is what the divide and conquer needs.

It is the largest prime below $2^{30}$, chosen so that products of two residues fit in 64 bits.

$998244353 = 7 \cdot 17 \cdot 2^{23} + 1$, so $2^{23}$ divides $p - 1$.

$3$ is a primitive root modulo $998244353$.

It is a Mersenne prime, so reduction modulo it is a shift and an add.