Coprime picking game on the integers 2 to 30

Two players, Alice and Bob, alternately pick integers from $\{2,3,\dots,30\}$. Whoever first picks a number having a common factor greater than $1$ with some number already chosen loses. Alice may decide whether she moves first or second, and both play perfectly. Put $p=1$ if Alice should move first and $p=2$ if she should move second. It turns out Alice has exactly six winning opening picks $v_1,\dots,v_6$. Compute $100p+\dfrac{v_1+\cdots+v_6}{6}$.

115. Alice should start ($p=1$). Picking $6$ (or $12,18,24$) kills primes $2$ and $3$; after that every remaining safe number uses exactly one of the $8$ primes $5,\dots,29$, so moves just knock out one prime each and Bob runs out first. Opening with $5$ or $25$ also wins (confirmed by exhaustive search), giving $100+\tfrac{6+12+18+24+5+25}{6}=115$.