diff --git a/base/random/RNGs.jl b/base/random/RNGs.jl
index f3e6602411bd1..35ed9245e2166 100644
--- a/base/random/RNGs.jl
+++ b/base/random/RNGs.jl
@@ -67,17 +67,19 @@ mutable struct MersenneTwister <: AbstractRNG
     state::DSFMT_state
     vals::Vector{Float64}
     idx::Int
+    advance::BigInt
+    advance_last_vals::BigInt
 
-    function MersenneTwister(seed, state, vals, idx)
+    function MersenneTwister(seed, state, vals, idx, advance, advance_last_vals)
         length(vals) == MTCacheLength && 0 <= idx <= MTCacheLength ||
             throw(DomainError((length(vals), idx),
                       "`length(vals)` and `idx` must be consistent with $MTCacheLength"))
-        new(seed, state, vals, idx)
+        new(seed, state, vals, idx, advance, advance_last_vals)
     end
 end
 
 MersenneTwister(seed::Vector{UInt32}, state::DSFMT_state) =
-    MersenneTwister(seed, state, zeros(Float64, MTCacheLength), MTCacheLength)
+    MersenneTwister(seed, state, zeros(Float64, MTCacheLength), MTCacheLength, 0, 0)
 
 """
     MersenneTwister(seed)
@@ -134,7 +136,7 @@ copy(src::MersenneTwister) =
 hash(r::MersenneTwister, h::UInt) = foldr(hash, h, (r.seed, r.state, r.vals, r.idx))
 
 show(io::IO, rng::MersenneTwister) =
-    print(io, "MersenneTwister RNG with seed 0x$(hex(from_seed(m.seed)))")
+    print(io, "MersenneTwister(0x$(hex(from_seed(rng.seed))), $(rng.advance), $(rng.advance_last_vals), $(rng.idx))")
 
 
 ### low level API
@@ -146,7 +148,8 @@ mt_setempty!(r::MersenneTwister) = r.idx = MTCacheLength
 mt_pop!(r::MersenneTwister) = @inbounds return r.vals[r.idx+=1]
 
 function gen_rand(r::MersenneTwister)
-    @gc_preserve r dsfmt_fill_array_close1_open2!(r.state, pointer(r.vals), length(r.vals))
+    MPZ.set!(r.advance_last_vals, r.advance)
+    @gc_preserve r fill_array!(r, pointer(r.vals), length(r.vals), Close1Open2())
     mt_setfull!(r)
 end
 
@@ -337,6 +340,11 @@ function _rand_max383!(r::MersenneTwister, A::UnsafeView{Float64}, I::FloatInter
     A
 end
 
+function fill_array!(rng::MersenneTwister, A::Ptr{Float64}, n::Int, I)
+    MPZ.add_ui!(rng.advance, n)
+    #rng.advance += n
+    fill_array!(rng.state, A, n, I)
+end
 
 fill_array!(s::DSFMT_state, A::Ptr{Float64}, n::Int, ::CloseOpen_64) =
     dsfmt_fill_array_close_open!(s, A, n)
@@ -361,10 +369,10 @@ function rand!(r::MersenneTwister, A::UnsafeView{Float64},
     align = Csize_t(pA) % 16
     if align > 0
         pA2 = pA + 16 - align
-        fill_array!(r.state, pA2, n2, I[]) # generate the data in-place, but shifted
+        fill_array!(r, pA2, n2, I[]) # generate the data in-place, but shifted
         unsafe_copyto!(pA, pA2, n2) # move the data to the beginning of the array
     else
-        fill_array!(r.state, pA, n2, I[])
+        fill_array!(r, pA, n2, I[])
     end
     for i=n2+1:n
         A[i] = rand(r, I[])
@@ -501,7 +509,9 @@ function randjump(mt::MersenneTwister, jumps::Integer, jumppoly::AbstractString)
     push!(mts, mt)
     for i in 1:jumps-1
         cmt = mts[end]
-        push!(mts, MersenneTwister(copy(cmt.seed), dSFMT.dsfmt_jump(cmt.state, jumppoly)))
+        newrng = MersenneTwister(copy(cmt.seed), dSFMT.dsfmt_jump(cmt.state, jumppoly))
+        MPZ.set_ui!(newrng.advance, Int64(10)^20)
+        push!(mts, newrng)
     end
     return mts
 end
diff --git a/base/random/random.jl b/base/random/random.jl
index 6ed336d2e4412..0281d5f0cef7b 100644
--- a/base/random/random.jl
+++ b/base/random/random.jl
@@ -227,6 +227,8 @@ rand(                ::Type{X}, d::Integer, dims::Integer...) where {X} = rand(X
 function __init__()
     try
         srand()
+        GLOBAL_RNG.advance = big(0)
+        GLOBAL_RNG.advance_last_vals = big(0)
     catch ex
         Base.showerror_nostdio(ex,
             "WARNING: Error during initialization of module Random")