I found this in the code - looks like it's based on 10^(sqrt(log10(beauty / 100B)))
prestigeGain: (state, getters, rootState, rootGetters) => {
if (rootState.stat.gallery_beauty.value < buildNum(1, 'T')) {
return 0;
}
return Math.floor(rootGetters['mult/get']('currencyGalleryCashGain', Math.pow(10, Math.pow(logBase(rootState.stat.gallery_beauty.value / buildNum(100, 'B'), 10), 0.5))));
},