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weakly primes
A prime that cannot be changed into another prime by changing a single digit. more

The first 600 weakly primes :
294001, 505447, 584141, 604171, 971767, 1062599, 1282529, 1524181, 2017963, 2474431, 2690201, 3085553, 3326489, 4393139, 5152507, 5564453, 5575259, 6173731, 6191371, 6236179, 6463267, 6712591, 7204777, 7469789, 7469797, 7858771, 7982543, 8090057, 8353427, 8532761, 8639089, 9016079, 9537371, 9608189, 9931447, 10506191, 10564877, 11124403, 11593019, 12325739, 14075273, 14090887, 14151757, 15973733, 16497121, 17412427, 17412599, 17424721, 18561293, 18953677, 19851991, 20212327, 20414561, 21044557, 21089489, 21281479, 21496661, 21668839, 21717601, 22138349, 22431391, 22480351, 23228479, 23274191, 23462969, 25081361, 25151927, 25475617, 25556941, 25768091, 25872199, 25948847, 26024267, 26521721, 27242179, 27245539, 27425521, 27465103, 27469241, 28046353, 28070047, 28978889, 29136091, 29348797, 29638519, 30791767, 30915637, 30964013, 31240481, 32524313, 33051769, 34302127, 34349969, 34586371, 35009671, 35319367, 35355923, 35673679, 35954509, 36221597, 37074487, 37095427, 37448137, 38178211, 38530123, 39397009, 39689597, 39724417, 40085977, 40432489, 40638727, 40812781, 41745331, 41980441, 42120581, 42145837, 42758917, 43414669, 43432409, 43924399, 43988459, 44617561, 44750351, 45420457, 46031123, 46301219, 46448719, 46591507, 47263001, 47457367, 47744239, 48024359, 48143047, 48341959, 48384977, 48441331, 49259803, 49353841, 49453847, 50030077, 50170513, 50413439, 50456519, 50471857, 50592911, 50729603, 51340909, 52127189, 53355689, 53420963, 53454589, 53751119, 53753587, 53977403, 54048263, 54292081, 54559123, 54868459, 55204889, 55959643, 56485057, 56660599, 56690071, 56743469, 57013823, 57177889, 57375139, 57980963, 58020581, 58091653, 58107953, 58366619, 58572593, 59088739, 59160317, 59704529, 60949807, 61089089, 61552901, 61575539, 61589579, 62324861, 62444033, 62552489, 62725253, 63359161, 64085921, 64087411, 64843237, 65029997, 65040751, 65314439, 65366051, 65702393, 65947213, 66117679, 66640253, 66854549, 67296517, 67489091, 67715653, 67959743, 68030449, 68428379, 68495347, 68970457, 69315427, 69374167, 69505109, 69912431, 70006253, 70078549, 70514141, 70717291, 70850641, 71364053, 71370853, 71756029, 71760109, 72168857, 72418187, 72422393, 72504457, 72519631, 72673213, 72760297, 73022273, 73179193, 73440439, 73644101, 74143801, 74190419, 74543663, 74711779, 75374149, 75448801, 75460849, 76297087, 76456141, 76720291, 76828823, 77250497, 77438461, 77444701, 77511487, 77540017, 77675639, 77844287, 78050209, 78440119, 78562307, 78712681, 78958211, 79477127, 79833133, 80054363, 80286407, 80468587, 81397777, 81434501, 81536501, 81608981, 81811589, 82087813, 82319411, 82542419, 82742243, 82764371, 82817039, 82892633, 82905047, 83127119, 83407327, 83610599, 83880829, 84083011, 84159917, 84255251, 84487439, 84733919, 85415249, 85468223, 85478369, 85637089, 86504879, 86688269, 87055763, 87303817, 87517271, 87615019, 88551439, 88826693, 88903379, 88948439, 89006641, 89146619, 89473777, 89602771, 89819413, 90997241, 92027977, 92305589, 92519951, 92782441, 93573091, 93831383, 94113781, 94874159, 94912583, 95401417, 95517517, 95532289, 95663761, 95992103, 97069493, 97165001, 97283321, 97353379, 97518247, 97551143, 97792117, 97864961, 97994641, 98285017, 98372203, 98451193, 98643439, 98701003, 98750609, 98954621, 99041179, 99157987, 99595919, 99778351, 100447177, 101154751, 101413777, 102871081, 103291453, 104097043, 104908273, 105217711, 106086811, 106371787, 107552111, 108903143, 110548133, 111033269, 111438259, 111522709, 111627713, 111974587, 112602443, 112663181, 113130803, 113290007, 115610399, 116061419, 116297257, 116321323, 117302429, 118121197, 118565423, 118966829, 119050499, 119075857, 119686943, 122047117, 122150891, 122773549, 123892907, 125286191, 126270601, 126445639, 126517543, 126772411, 127311133, 128456557, 128824391, 128885389, 129461279, 130859077, 131022547, 131739043, 132077149, 134143837, 134528677, 135085453, 135272429, 135345391, 135870139, 136003643, 136240781, 136562467, 137083109, 137165071, 137813021, 138583811, 139281463, 139452133, 139806203, 140383207, 141016331, 141017011, 141187097, 141307483, 142095827, 142380013, 142790317, 143561773, 143924173, 144232247, 144442087, 144481273, 144536701, 144988267, 146020961, 146610701, 147826829, 147846253, 148421633, 148974047, 149411569, 149480959, 150175379, 150971243, 151187611, 151753867, 154114031, 154377841, 154467277, 154477891, 155498891, 156148427, 156251789, 156303463, 156394657, 156589987, 156693529, 157018483, 157101907, 157553993, 159290381, 161423527, 162066193, 162123869, 162417733, 162524249, 162630497, 163146457, 163482377, 163655431, 164076173, 164262151, 164787449, 165543479, 165600647, 165613871, 165656159, 165862253, 165994513, 166374487, 167056709, 167637101, 167753561, 168956971, 169567081, 169817047, 170448713, 170880299, 171154673, 171206471, 171310747, 172155173, 172535497, 173011789, 173050477, 173485307, 173854783, 174163679, 174465541, 174615391, 175110097, 175164643, 175489417, 175539191, 175988881, 176582687, 176598493, 176704379, 177704491, 177911983, 178014517, 180044797, 180455519, 180552809, 181475743, 181946617, 182363249, 182386921, 183585973, 183838177, 183855059, 183875191, 184116337, 184972289, 185627177, 185823727, 186000169, 186343193, 187558759, 187750883, 188756171, 189525311, 189895879, 190056833, 190530629, 191139671, 192093787, 192855583, 193837841, 194437163, 194512459, 194846149, 195315619, 196363373, 196389047, 197611483, 197964253, 198129871, 198303601, 198764771, 198873523, 199802621, 200410643, 200875271, 201067729, 201674041, 202172063, 202607243, 204677017, 206375471, 206461007, 206845729, 207091853, 207751811, 207773861, 208017679, 208278557, 209297449, 209538169, 209769991, 210362171, 211848541, 212040557, 212083709, 212470087, 212545831, 213685123, 214374443, 215329753, 215723539, 215962031, 216553829, 216575111, 216826097, 217870921, 217974623, 218730991, 218803751, 219149123, 219172579, 219438257, 219688867, 219972637, 220176029, 220556603, 221147131, 221758003, 221944409, 222626231, 222638237, 222696457, 222883571, 222914941, 223182941, 223404989, 223646447, 224398087, 224455391, 224545759, 224709337, 225113981, 225265883, 225761299, 226122881, 227652493, 228107927, 228661457, 228999007.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 318177 values, from 294001 to 99999446179).

n\r 0  1 
20318177 2 
30159815158362 3 
401591200159057 4 
5080081790927912279882 5 
60159815000158362 6 
70555355231251842508915380453793 7 
8079696079657079424079400 8 
9053529523190532205301305306653030 9 
1008008107912200079092079882 10 
11023474263914693825318369173754525325464112642023438

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.