diff --git a/src/Primes.jl b/src/Primes.jl
index fa9a916..1241201 100644
--- a/src/Primes.jl
+++ b/src/Primes.jl
@@ -108,7 +108,7 @@ function primes(lo::Int, hi::Int)
     lo ≤ 3 ≤ hi && push!(list, 3)
     lo ≤ 5 ≤ hi && push!(list, 5)
     hi < 7 && return list
-    sizehint!(list, floor(Int, hi / log(hi)))
+    sizehint!(list,  5 + floor(Int, hi / (log(hi) - 1.12) -  lo / (log(max(lo,2)) - 1.12*(lo > 7))) ) # http://projecteuclid.org/euclid.rmjm/1181070157    
     sieve = _primesmask(max(7, lo), hi)
     lwi = wheel_index(lo - 1)
     @inbounds for i = 1:length(sieve)   # don't use eachindex here
diff --git a/test/runtests.jl b/test/runtests.jl
index 3fbf83f..ae0f7c5 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -182,6 +182,10 @@ for n = 1:100
     @test n == m
 end
 
+let i = rand(1:2^(3*min(WORD_SIZE,64)÷4)) 
+    @test primes(i,i+300) == filter(isprime, i:i + 300) == filter(isprime, big(i:i + 300))
+end
+
 
 @test isprime(BigInt(1000000007))
 @test isprime(BigInt(1000000007), 1)