diff --git a/basis/math/primes/erato/erato-docs.factor b/basis/math/primes/erato/erato-docs.factor
index 75e3846dc1..b9d9ea38df 100644
--- a/basis/math/primes/erato/erato-docs.factor
+++ b/basis/math/primes/erato/erato-docs.factor
@@ -1,10 +1,14 @@
-USING: help.markup help.syntax ;
+USING: byte-arrays help.markup help.syntax kernel math ;
 IN: math.primes.erato
 
 HELP: sieve
-{ $values { "n" "the greatest odd number to consider" } { "arr" "a bit array" } }
-{ $description "Apply Eratostene sieve up to " { $snippet "n" } ". Primality can then be tested using " { $link marked-prime? } "." } ;
+{ $values { "n" integer } { "arr" byte-array } }
+{ $description "Apply Eratostene sieve up to " { $snippet "n" }
+". " { $snippet "n" } " must be greater than 1"
+". Primality can then be tested using " { $link marked-prime? } "." } ;
 
 HELP: marked-prime?
-{ $values { "n" "an integer" } { "arr" "a byte array returned by " { $link sieve } } { "?" "a boolean" } }
-{ $description "Check whether an odd integer between 3 and the limit given to " { $link sieve } " has been marked as a prime number."} ;
+{ $values { "n" integer } { "arr" byte-array } { "?" boolean } }
+{ $description "Checks whether " { $snippet "n" } " has been marked as a prime number. "
+{ $snippet "arr" } " must be " { $instance byte-array } " returned by " { $link sieve } ". "
+{ $snippet "n" } " must be between 2 and the limit given to " { $link sieve } "." } ;
diff --git a/basis/math/primes/erato/erato-tests.factor b/basis/math/primes/erato/erato-tests.factor
index e6f7765bd6..ff44ec2210 100644
--- a/basis/math/primes/erato/erato-tests.factor
+++ b/basis/math/primes/erato/erato-tests.factor
@@ -1,4 +1,5 @@
-USING: byte-arrays math math.bitwise math.primes.erato sequences tools.test ;
+USING: kernel byte-arrays sequences tools.test ;
+USING: math math.bitwise math.ranges math.primes.erato ;
 
 [ B{ 255 251 247 126 } ] [ 100 sieve ] unit-test
 [ 1 100 sieve marked-prime? ] [ bounds-error? ] must-fail-with
@@ -8,3 +9,8 @@ USING: byte-arrays math math.bitwise math.primes.erato sequences tools.test ;
 
 ! There are 25997 primes below 300000. 1 must be removed and 3 5 7 added.
 [ 25997 ] [ 299999 sieve [ bit-count ] map-sum 2 + ] unit-test
+
+! Check sieve array length logic by making sure we get the right
+! end-point for numbers with all possibilities mod 30. If something
+! were to go wrong, we'd get a bounds-error.
+[ ] [ 2 100 [a,b] [ dup sieve marked-prime? drop ] each ] unit-test
diff --git a/basis/math/primes/erato/erato.factor b/basis/math/primes/erato/erato.factor
index fdc2f9fc3b..4df724cfc2 100644
--- a/basis/math/primes/erato/erato.factor
+++ b/basis/math/primes/erato/erato.factor
@@ -28,7 +28,7 @@ CONSTANT: masks B{ 0 128 0 0 0 0 0 64 0 0 0 32 0 16 0 0 0 8 0 4 0 0 0 2 0 0 0 0
         2drop
     ] if ;
 
-: init-sieve ( n -- arr ) 29 + 30 /i 255 <array> >byte-array ;
+: init-sieve ( n -- arr ) 30 /i 1 + 255 <array> >byte-array ;
 
 PRIVATE>