Steel for a mold and mold

A steel for a mold, having a composition consisting of, on % by mass basis:

• 0.55%≤C≤0.70%;
• 0.30%≤Si≤0.60%;
• 0.55%≤Mn≤1.2%;
• 5.7%≤Cr≤6.9%;
• 1.2%≤Mo+W/2≤1.6%;
• 0.55%≤V≤0.79%;
• 0.005%≤N≤0.1%,
• Nb≤0.5%;
• Zr≤0.5%;
• Ta≤0.5%;
• and
• Co≤1.0%,
• with the remainder being Fe and inevitable impurities satisfying, on % by mass basis, Al≤0.020%, Ni≤0.20%, S≤0.0015%, and Cu≤0.10%, and
• satisfying P1≥24 and 4.9≤P2≤7.3, P1 being a value obtained based on the following formula (1) and P2 being a value obtained based on the following formula (2),
• P1=45−13.6[Si]−7.0([Mo]+[W]/2)−12.9[Ni] (1)
• P2=7.4[V]+15.8[N]+38.6[Al] (2)
• in the formulae (1) and (2), [M] represents a content of an element M in % by mass basis,
• wherein in a state after quenching and tempering, the steel has a hardness at room temperature of 58 HRC or more and 61 HRC or less, and a thermal conductivity at room temperature of 20 W/(m·K) or more, and
• in a state after quenching, the steel has a crystal grain size of 5 or more in terms of a grain size number defined in JIS G 0551:2020.