3XE is the largest known Wilson prime, the only other two known Wilson primes are 5 (the smallest number not dividing 10) and 11 (the smallest number > 10).

3XE is the Sierpinski base ≤1000 for which 10 is a Sierpinski number (i.e. 10×3XE^n+1 is composite for all n≥1) and with most primes in the covering set ({5, 7, 11, 17, 25}), exactly the primes whose reciprocal has period 2, 4, or 6 (also dividing 10 and >1, but the only prime with period 3 (111) and the only prime with period 10 (EE01) are both too large) (thus, there is no k≥1 such that concatenation of 3XE^k and 1 is prime, the numbers n such that there is no k≥1 such that concatenation of n^k and 1 is prime are (except power of 10, which corresponding to generalized Fermat primes base 10) 12, 23, 34, 45, 56, 67, 78, 89, 9X, XE, EX, 100, 111, 122, 133, 144, 155, 166, 177, 188, 199, 1XX, 1E9, 1EE, 208, 210, 221, 232, 243, 254, 265, 276, 287, 298, 2X9, 2E8, 2EX, 30E, 320, 331, 342, 353, 364, 375, 386, 397, 3X8, 3XX, 3XE, 3E7, 3E9, ..., they are the numbers of the form 11m+1 (which has a covering set {11}) or EEm−1 (which has a covering set {E, 11}), plus some other numbers (208, 3XX, 3XE, 419, 590, 630, 631, 812, 9E5 (less than 1000)), there are six numbers (less than 400) which might be (but very unlikely) in this sequence: 117, 153, 256, 262, 268, 340

Although 3XE×10^n+1 is not prime for all n≤2000. but 3XE is not base 10 Sierpinski number, the smallest n such that 3XE×10^n+1 is prime is 23E0 (thus, 3XE0n1 (i.e. 3XE000...0001 with n 0's) is not prime until the number 3XE023XE1)

3XE followed by 3XE 1’s is prime, note that 3XE followed by n 1’s is not prime for all n<374

3XE is strobogrammatic prime.

3XE is the smallest prime p such that the aliquot sequence for p^2 has not yet been fully determined.