The (probable) primes from the next list of pandigitals
(split into 4-digit factorials and a displacement of the remaining 6 digits)
must have prime displacements (both positive and negative).
ps. the same is true for the ninedigital case (resp. 4 and 5 digits)
(also known as 'zeroless pandigital').
Suppose we have a composite displacement then we could split it
into its factors. One of the factors of this 6-digit number is always smaller
than the factorial number itself and hence we can extract a common factor:
[ 1*2*3*4*...*(n-1)*(n) ] +/- [ f1*...*fn ]
[ cf ] * [ [ 1*2*3*4*...*(n-1)*(n) ] +/- [ f1*...*fn ] ]
rendering the whole shebang divisible by this common factor
yielding no longer a (probable) prime but a composite.
Hence the 6-digit displacement itself must be prime as well !
A smallest composite in this (probable) prime expression must be a 7-digit displacement.

For reference goals and easy searching all the nine- & pandigitals
implicitly displayed in these topics are listed here.

Topic → 1024865937, 1025978643, 1039684527, 1058643927, 1064295387, 1072548693,
1208657439, 1208749653, 1237468509, 1249560873, 1256348097, 1267408953, 1268903457,
1295368047, 1409583267, 1463805297, 1468205937, 1478965023, 1486530279, 1538762049,
1538942607, 1564930827, 1580672349, 1604259837, 1609825347, 1642857039, 1652807493,
1750829463, 1768205493, 1805673429, 1825640973, 1840726953, 1894326057, 2015483697,
2035748169, 2063548719, 2086547139, 2086759431, 2087615493, 2095816743, 2165340897,
2354810697, 2486375019, 2518306479, 2546983701, 2569410387, 2659704183, 2675438091,
2678103549, 2684571093, 2690351847, 2690743851, 2710568349, 2896570413, 2906875341,
2915608347, 2945837601, 2957403861, 2960174583, 3052681497, 3526907481, 3574810269,
3640528719, 3815764209, 3865970421, 3965214087, 4012583697, 4087356129, 4093257861,
4237608591, 4607235891, 4670582391, 4682701359, 4802659173, 4805237691, 4829176503,
4895271603, 4910528673, 4985610327, 5347689201, 5380241679, 5710968423, 5806197243,
5906128347, 6014253789, 6095184273, 6104283957, 6184302759, 6271450839, 6502734189,
6835104729, 6850342791, 6985270143, 7015948263, 7168530249, 7261458309, 7268903451,
7528436091, 7540863921, 7618450239, 8206159437, 8294306157, 8362159407, 8527149603,
8734596021, 8975402631, 9031268547.
1028465739, 1048362759, 1048659237, 1052643879, 1063254987, 1072498653, 1096523847,
1204879653, 1204936587, 1268593407, 1270584963, 1304869257, 1342680597, 1432589607,
1459678203, 1468523907, 1507426389, 1508763429, 1582490367, 1670348259, 1685432907,
1702583469, 1832640957, 1867590243, 2015684379, 2018765439, 2056871349, 2183695407,
2390547681, 2459103867, 2485106397, 2495867301, 2531409867, 2543160879, 2564138079,
2584136709, 2609475381, 2689470531, 2701985463, 2738450691, 2759608431, 2851637409,
2930586471, 2960785143, 3046217859, 3062147859, 3098642517, 3280459167, 3406982571,
3421658079, 3460192587, 3470651289, 3520768941, 3572468109, 3586192047, 3781264059,
3790845261, 3985276041, 4057398621, 4216578309, 4310756289, 4367258019, 4603297581,
4706581239, 4709128563, 4837216509, 4856709231, 5032741869, 5047812639, 5239618407,
5290861347, 5438276019, 5471283609, 5702136849, 5728903641, 5780921643, 5792864301,
5974610823, 6028734159, 6035784129, 6037182549, 6145238709, 6190875243, 6254738109,
6347518209, 6428350971, 6458213097, 6470583291, 6485137209, 6485203971, 6491782053,
6508273149, 6508973421, 6850423179, 7298643051, 7408162593, 7520968431, 7594620813,
7942305861, 7946302851, 8024756139, 8027143569, 8062473159, 8246390751, 8432610579,
8596240173, 8635217409, 8905217643, 9034856721, 9065413827, 9461520837, 9725380641,
9820617453, 9860715423.