in the range 991 < p < 10^175 the only base 10 permutable primes are repunit primes
I'll copy/paste from Arkadii Slinko's "Absolute Primes" (year?): Theorem 2: Let N be an absolute prime, different from repunits, that contains n > 3 digits in its decimal representation. Then n is a multiple of 11088. Proof: According to the previous lemma we assume that n > 16. Since 10 is a primitive root modulo 17, Lemma 6 yields that n divides 16 and hence n >= 32. We can repeat this argument three times, using the primes 19, 23, 29, to obtain that n is a multiple of 18, 22 and 28, respectively. Therefore n divides LCM(16,18,22,28) = 11088. Richert used in addition the primes 47, 59, 61, 97, 167, 179, 263, 383, 503, 863, 887, 983 to show that the number n of digits of the absolute prime number Bn(a,b) is divisible by 321653308662329838581993760. He also mentioned, that by using the tables of primes and their primitive roots up to 10^5, it is possible to show that n > 6*10^175.