claim_id,source,label,span
ts-claim-ps1-cramer-model-fails-at-two-scales,doi:10.1007/s00220-004-1222-4,SUPPORTS,"Contrary to what would be predicted on the basis of Cramér's model concerning the distribution of prime numbers, we develop evidence that the distribution of $ψ(x+H)- ψ(x)$, for $0\le x\le N$, is approximately normal with mean $\sim H$ and variance $\sim H\log N/H$, when $N^δ\le H \le N^{1-δ}$."