# Distribution of primes in smooth moduli

From Polymath1Wiki

A key input to Zhang's proof that bounded gaps occur infinitely often is a distribution result on primes in smooth moduli, which we have called [math]MPZ[\varpi,\delta][/math] (and later strengthened to [math]MPZ'[\varpi,\delta][/math]. These estimates are obtained as a combination of three other estimates, which we will call [math]Type_I[\varpi,\delta,\sigma][/math], [math]Type_{II}[\varpi,\delta,\sigma][/math], and [math]Type_{III}[\varpi,\delta,\sigma][/math].