upto(qdigits) = {my(copr30 = select(x -> gcd(x, 30) == 1, [1..30], 1)); ulim = sqrtint(10^(qdigits)); res = List(); t = 0; u = 1000; 
i = 7; 
while(i <= ulim, 
	s = i^2; t++; if(t > u, print1(i", "); u += 1000); 
	qd = #digits(i); 
	for(j = qd + 1, qdigits, 
		process(s, j); 
	); i++; 
	while(gcd(i, 30) > 1, i++); 	 
); listsort(res); res
}

process(s, n) = {my(i, d = digits(s), x = vector(#d, i, [2, n-1]), w = vector(n)); if(#select(z -> !z, d) > 0, return); x[1] = [1, 1]; x[#d] = [n, n]; w[1] = d[1]; w[n] = d[#d]; 
forvec(v = x, 
	cw = w;
	for(i = 2, #d - 1, 
		cw[v[i]] = d[i]; 
	); fr = fromdigits(cw);  
	if(isprime(fr), listput(res, fr)) 
,
2
)
}