diff --git a/extra/project-euler/003/003.factor b/extra/project-euler/003/003.factor
index 87db922e5f..2b229aa11b 100644
--- a/extra/project-euler/003/003.factor
+++ b/extra/project-euler/003/003.factor
@@ -1,6 +1,6 @@
 ! Copyright (c) 2007 Aaron Schaefer.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math project-euler.common sequences ;
+USING: math.primes.factors sequences ;
 IN: project-euler.003
 
 ! http://projecteuler.net/index.php?section=problems&id=3
@@ -17,12 +17,12 @@ IN: project-euler.003
 ! --------
 
 : largest-prime-factor ( n -- factor )
-    prime-factors supremum ;
+  factors supremum ;
 
 : euler003 ( -- answer )
-    317584931803 largest-prime-factor ;
+  317584931803 largest-prime-factor ;
 
-! [ euler003 ] 100 ave-time
-! 404 ms run / 9 ms GC ave time - 100 trials
+! [ euler003 ] time
+! 2 ms run / 0 ms GC time
 
 MAIN: euler003
diff --git a/extra/project-euler/007/007.factor b/extra/project-euler/007/007.factor
index 0a9cd98865..12f06972a9 100644
--- a/extra/project-euler/007/007.factor
+++ b/extra/project-euler/007/007.factor
@@ -1,6 +1,6 @@
 ! Copyright (c) 2007 Aaron Schaefer.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: kernel math math.miller-rabin ;
+USING: lazy-lists math math.primes ;
 IN: project-euler.007
 
 ! http://projecteuler.net/index.php?section=problems&id=7
@@ -18,12 +18,12 @@ IN: project-euler.007
 ! --------
 
 : nth-prime ( n -- n )
-    2 swap 1- [ next-prime ] times ;
+  1 - lprimes lnth ;
 
 : euler007 ( -- answer )
-    10001 nth-prime ;
+  10001 nth-prime ;
 
 ! [ euler007 ] time
-! 19230 ms run / 487 ms GC time
+! 22 ms run / 0 ms GC time
 
 MAIN: euler007
diff --git a/extra/project-euler/010/010.factor b/extra/project-euler/010/010.factor
index 055e902776..e22d3bc39c 100644
--- a/extra/project-euler/010/010.factor
+++ b/extra/project-euler/010/010.factor
@@ -1,7 +1,6 @@
 ! Copyright (c) 2007 Aaron Schaefer, Samuel Tardieu.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: arrays kernel lazy-lists math math.erato math.functions math.ranges
-       namespaces sequences ;
+USING: math.primes sequences ;
 IN: project-euler.010
 
 ! http://projecteuler.net/index.php?section=problems&id=10
@@ -17,12 +16,12 @@ IN: project-euler.010
 ! SOLUTION
 ! --------
 
-! Sieve of Eratosthenes and lazy summing
+! Summing of prime numbers
 
 : euler010 ( -- answer )
-    0 1000000 lerato [ + ] leach ;
+  1000000 primes-upto sum ;
 
-! [ euler010 ] time
-! 765 ms run / 7 ms GC time
+! [ euler010 ] 100 ave-time
+! 14 ms run / 0 ms GC ave time - 100 trials
 
 MAIN: euler010
diff --git a/extra/project-euler/134/134.factor b/extra/project-euler/134/134.factor
index b30b0073d2..90d8404760 100644
--- a/extra/project-euler/134/134.factor
+++ b/extra/project-euler/134/134.factor
@@ -1,6 +1,6 @@
 ! Copyright (c) 2007 Samuel Tardieu.
 ! See http://factorcode.org/license.txt for BSD license.
-USING: arrays kernel math.algebra math math.functions math.primes.list
+USING: arrays kernel lazy-lists math.algebra math math.functions math.primes
        math.ranges sequences ;
 IN: project-euler.134
 
@@ -23,9 +23,9 @@ IN: project-euler.134
 ! SOLUTION
 ! --------
 
-! Compute the smallest power of 10 greater than m
+! Compute the smallest power of 10 greater than m or equal to it
 : next-power-of-10 ( m -- n )
-  10 swap log 10 log / >integer [ 10 * ] times ; foldable
+  10 swap log 10 log / ceiling >integer ^ ; foldable
 
 ! Compute S for a given pair (p1, p2) -- that is the smallest positive
 ! number such that X = p1 [npt] and X = 0 [p2] (npt being the smallest
@@ -34,7 +34,7 @@ IN: project-euler.134
   over 0 2array rot next-power-of-10 rot 2array chinese-remainder ;
 
 : euler134 ( -- answer )
-  primes-under-million 2 tail dup 1 tail 1000003 add  [ s ] 2map sum ;
+  5 lprimes-from [ 1000000 > ] luntil [ [ s + ] keep ] leach drop ;
 
 ! [ euler134 ] 10 ave-time
 ! 6743 ms run / 79 ms GC ave time - 10 trials