two integrals and a question about prime trinomials

[Eric W. Weisstein]

I anyone able to get the following two integrals in closed form?

Integrate[Exp[-2x^2]Erf[x]^2,{x,0,Infinity}]
Integrate[Exp[-x^2]Erf[x]^3/x,{x,0,Infinity}]

(I'm not.)

Also, Jonathan Vos Post and Robert G. Wilson have noted that there are a
dearth of prime central trinomial coefficients
http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=A002426
after n=4.  In fact, I just did a quick check and there are no others
besides n=2, 3, 4 up to n = 12,000.  Can someone prove that A002426(n) is
actually composite for all n>4?

Cheers,
-Eric