diff --git a/basis/math/primes/miller-rabin/miller-rabin-docs.factor b/basis/math/primes/miller-rabin/miller-rabin-docs.factor
index 4aa318f674..2455dafdd5 100644
--- a/basis/math/primes/miller-rabin/miller-rabin-docs.factor
+++ b/basis/math/primes/miller-rabin/miller-rabin-docs.factor
@@ -1,7 +1,7 @@
 ! Copyright (C) 2009 Doug Coleman.
 ! See http://factorcode.org/license.txt for BSD license.
 USING: help.markup help.syntax kernel sequences math ;
-IN: math.miller-rabin
+IN: math.primes.miller-rabin
 
 HELP: find-relative-prime
 { $values
@@ -82,8 +82,8 @@ HELP: unique-primes
 }
 { $description "Generates a sequence of " { $snippet "n" } " unique prime numbers with exactly " { $snippet "numbits" } " bits." } ;
 
-ARTICLE: "math.miller-rabin" "Miller-Rabin probabilistic primality test"
-"The " { $vocab-link "math.miller-rabin" } " vocabulary implements the Miller-Rabin probabilistic primality test and utility words that use it in order to generate random prime numbers." $nl
+ARTICLE: "math.primes.miller-rabin" "Miller-Rabin probabilistic primality test"
+"The " { $vocab-link "math.primes.miller-rabin" } " vocabulary implements the Miller-Rabin probabilistic primality test and utility words that use it in order to generate random prime numbers." $nl
 "The Miller-Rabin probabilistic primality test:"
 { $subsection miller-rabin }
 { $subsection miller-rabin* }
@@ -97,4 +97,4 @@ ARTICLE: "math.miller-rabin" "Miller-Rabin probabilistic primality test"
 { $subsection next-safe-prime }
 { $subsection random-safe-prime } ;
 
-ABOUT: "math.miller-rabin"
+ABOUT: "math.primes.miller-rabin"
diff --git a/basis/math/primes/miller-rabin/miller-rabin-tests.factor b/basis/math/primes/miller-rabin/miller-rabin-tests.factor
index 9981064ec0..9c635c8f38 100644
--- a/basis/math/primes/miller-rabin/miller-rabin-tests.factor
+++ b/basis/math/primes/miller-rabin/miller-rabin-tests.factor
@@ -1,6 +1,6 @@
-USING: math.miller-rabin tools.test kernel sequences
-math.miller-rabin.private math ;
-IN: math.miller-rabin.tests
+USING: math.primes.miller-rabin tools.test kernel sequences
+math.primes.miller-rabin.private math ;
+IN: math.primes.miller-rabin.tests
 
 [ f ] [ 473155932665450549999756893736999469773678960651272093993257221235459777950185377130233556540099119926369437865330559863 miller-rabin ] unit-test
 [ t ] [ 2 miller-rabin ] unit-test
diff --git a/basis/math/primes/miller-rabin/miller-rabin.factor b/basis/math/primes/miller-rabin/miller-rabin.factor
index 991924dfe4..35ee97a897 100755
--- a/basis/math/primes/miller-rabin/miller-rabin.factor
+++ b/basis/math/primes/miller-rabin/miller-rabin.factor
@@ -3,7 +3,7 @@
 USING: combinators kernel locals math math.functions math.ranges
 random sequences sets combinators.short-circuit math.bitwise
 math math.order ;
-IN: math.miller-rabin
+IN: math.primes.miller-rabin
 
 : >odd ( n -- int ) 0 set-bit ; foldable
 
diff --git a/basis/math/primes/primes.factor b/basis/math/primes/primes.factor
index 688fdad713..fa1cd5cb63 100644
--- a/basis/math/primes/primes.factor
+++ b/basis/math/primes/primes.factor
@@ -1,7 +1,8 @@
 ! Copyright (C) 2007-2009 Samuel Tardieu.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: combinators kernel math math.functions math.miller-rabin
-math.order math.primes.erato math.ranges sequences ;
+USING: combinators kernel math math.functions
+math.primes.miller-rabin math.order math.primes.erato
+math.ranges sequences ;
 IN: math.primes
 
 <PRIVATE
diff --git a/extra/crypto/rsa/rsa.factor b/extra/crypto/rsa/rsa.factor
index 373dd9637c..1da170d197 100644
--- a/extra/crypto/rsa/rsa.factor
+++ b/extra/crypto/rsa/rsa.factor
@@ -1,7 +1,7 @@
 ! Copyright (C) 2008 Doug Coleman.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: math.miller-rabin kernel math math.functions namespaces
-sequences accessors ;
+USING: math.primes.miller-rabin kernel math math.functions
+namespaces sequences accessors ;
 IN: crypto.rsa
 
 ! The private key is the only secret.
diff --git a/extra/project-euler/common/common.factor b/extra/project-euler/common/common.factor
index c2ffe26d94..84291f2ce8 100644
--- a/extra/project-euler/common/common.factor
+++ b/extra/project-euler/common/common.factor
@@ -1,7 +1,7 @@
 ! Copyright (c) 2007-2009 Aaron Schaefer.
 ! See http://factorcode.org/license.txt for BSD license.
 USING: accessors arrays kernel lists make math math.functions math.matrices
-    math.miller-rabin math.order math.parser math.primes.factors
+    math.primes.miller-rabin math.order math.parser math.primes.factors
     math.primes.lists math.ranges math.ratios namespaces parser prettyprint
     quotations sequences sorting strings unicode.case vocabs vocabs.parser
     words ;
diff --git a/extra/random/blum-blum-shub/blum-blum-shub.factor b/extra/random/blum-blum-shub/blum-blum-shub.factor
index dc764fd040..4a52a2f79c 100755
--- a/extra/random/blum-blum-shub/blum-blum-shub.factor
+++ b/extra/random/blum-blum-shub/blum-blum-shub.factor
@@ -1,5 +1,5 @@
 USING: kernel math sequences namespaces
-math.miller-rabin math.functions accessors random ;
+math.primes.miller-rabin math.functions accessors random ;
 IN: random.blum-blum-shub
 
 ! Blum Blum Shub, n = pq, x_i+1 = x_i ^ 2 mod n