Here's my attempt which seems a little simpler than some of the others.
m[^ \d (?: (?<! \x20 ) \d | \x20 ){19} $]x
Which says that the entire string must constist of a digit followed by 19 ((digits not preceeded by spaces) or spaces).
print m[^ \d (?: (?<!\x20) \d | \x20 ){19} $]x
? 'Yes:' . $_
: ' No:' . $_
for @t;
No: 123451234512345
No: 123451234512345
Yes:123451234512345
Yes:1234512345
No:123 451 2345
No:
Examine what is said, not who speaks.
"Efficiency is intelligent laziness." -David Dunham
"Think for yourself!" - Abigail
Hooray!