[seqfan] Is A002144 identical to "primes in A020882 Ordered hypotenuses (with multiplicity) of primitive Pythagorean triangles?

[Jonathan Post]

Through 353, this is identical to "primes in A020882 Ordered
hypotenuses (with multiplicity) of primitive Pythagorean triangles.

A002144  	 	 Pythagorean primes: primes of form 4n+1.
(Formerly M3823 N1566) 	
	5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149,
157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313,
317, 337, 349, 353

I look through the b-list of the former, factorizing those with
multiplicity > 1.

Is there an easy proof that this is so?  That is, if the multiplicity
is >1 for the hypotenuse H of a primitive Pythagorean triangle, then H
must be composite?
The latter statement is true through H = 2329 = 17 * 137 .  Is this
obvious?  Is it interesting enough to be a comment to either seq?