“Mersenne-Twister”is default method for generating random number. The brief description is

“From Matsumoto and Nishimura (1998). A twisted GFSR with period *2^19937 – 1* and equidistribution in 623 consecutive dimensions (over the whole period). The ‘seed’ is a 624-dimensional set of 32-bit integers plus a current position in that set.”

At any given moment, “the current seed” is stored in “.Random.seed”. For a short example below, here is what the .Random.seed looks like.

> runif(5) [1] 0.5214241 0.6072482 0.8581209 0.1057113 0.4943451 > length(.Random.seed) [1] 626

# It is 626 long.

> head(.Random.seed) [1] 403 5 524275616 -891164866 839495241 2076756731 -695076150

# The first value is the type of random number generator, in this case “Mersenne-Twister”.

# The second value is the “current position” in the set

# The other 624 numbers stored in .Random.seed are what they call “seed”.

# So, if you simulated another 5 random numbers,

> runif(5) [1] 0.9766740 0.9481603 0.1786681 0.4026092 0.7110552

# The current position changed from 5 (above) to 10 (see below). Notice that other 624 numbers in the set remained the same.

> head(.Random.seed)

[1] 403 10 619611805 -1461824745 -1054662018 -1340796360

# Once you simulate 624th random number, the index of current position will be 624.

> runif(1)

[1] 0.8074707

> head(.Random.seed)

[1] 403 624 619611805 -1461824745 -1054662018 -1340796360

# When you simulate one more random number, a new seed will then be used.

> runif(1) [1] 0.6062263

> head(.Random.seed)

[1] 403 1 -1016206940 813281659 -1786346428 -363208600

# So, any given moment, you can save the current seed that will be used for the next simulation by

> my.seed <- .Random.seed > runif(10) [1] 0.8797226 0.2143323 0.6826555 0.4366940 0.4330555 0.5745667 0.7406138 0.4646236 0.8014502 0.9818474

# This saved the current seed to be used for the next simulation in “my.seed”

# You can then restore the current seed and reproduce the above simulated numbers by

> .Random.seed <- t(my.seed)

> runif(10)

[1] 0.8797226 0.2143323 0.6826555 0.4366940 0.4330555 0.5745667 0.7406138 0.4646236 0.8014502 0.9818474

# See that the runif(10) here gave the same numbers as the one above.