You could try a simple GP script to eliminate most k's:

For instance, (k*3^n+1)/2, we have the following k's remaining at n=3000:

[CODE]h=[]; for(i=1,3000, for(t=1,#g, if(ispseudoprime( (g[t]*3^i+1)/2 )==0, h=concat(h,g[t]);); ); g=h; h=[];)
[41, 821, 823, 935, 1187, 1801, 2747, 2909, 3007, 3047, 3061, 3307, 4495, 5147, 5321, 5743, 5893, 6041, 6427, 6569, 6575, 6967, 7297, 7927, 8161, 8227, 8389, 8467, 8609, 8863, 8987, 9061, 9263, 9449, 9721, 10207, 10243, 10741][/CODE]

PFGW would be a next step (with the -f switch) until you reach about 20k digits or so, you'd probably want to write a program or script which can support sieving these types of forms.

[QUOTE=carpetpool;547506]You could try a simple GP script to eliminate most k's:

For instance, (k*3^n+1)/2, we have the following k's remaining at n=3000:

[CODE]h=[]; for(i=1,3000, for(t=1,#g, if(ispseudoprime( (g[t]*3^i+1)/2 )==0, h=concat(h,g[t]);); ); g=h; h=[];)
[41, 821, 823, 935, 1187, 1801, 2747, 2909, 3007, 3047, 3061, 3307, 4495, 5147, 5321, 5743, 5893, 6041, 6427, 6569, 6575, 6967, 7297, 7927, 8161, 8227, 8389, 8467, 8609, 8863, 8987, 9061, 9263, 9449, 9721, 10207, 10243, 10741][/CODE]

PFGW would be a next step (with the -f switch) until you reach about 20k digits or so, you'd probably want to write a program or script which can support sieving these types of forms.[/QUOTE]

I have already tested them for bases 2<=b<=128 and 256, 512, 1024, see [URL="https://docs.google.com/document/d/e/2PACX-1vSbzPtWAyGntyR3WQO84qPkJA6uzGsRrNjUi0BYj-iNUzGsMbeeJ9-JixXFozfODnoa8lgHhw7d3mEX/pub"]https://docs.google.com/document/d/e/2PACX-1vSbzPtWAyGntyR3WQO84qPkJA6uzGsRrNjUi0BYj-iNUzGsMbeeJ9-JixXFozfODnoa8lgHhw7d3mEX/pub[/URL] (Sierpinski) and [URL="https://docs.google.com/document/d/e/2PACX-1vQb0b1YJBQOu00eot4UN6MncbFtAeLSfgtnK6EasdukCo4gHDMsw47ANKz-jhpArGFnFEXnvzcXZw9-/pub"]https://docs.google.com/document/d/e/2PACX-1vQb0b1YJBQOu00eot4UN6MncbFtAeLSfgtnK6EasdukCo4gHDMsw47ANKz-jhpArGFnFEXnvzcXZw9-/pub[/URL] (Riesel)

[QUOTE=sweety439;547502]SR124 done to n=10000

I know that for R124, some k's proven composite by partial algebra factors:

* All k where k = m^2 and m = = 2 or 3 mod 5
* All k where k = 31*m^2 and m = = 1 or 4 mod 5

but since there are too many such k, I didn't change the text file.[/QUOTE]

Update new file for R124

Update new zip file

S66 has there k remain for k<=10000:

{269, 470, 537, 1198, 1408, 1449, 2076, 2257, 2464, 2605, 2614, 2624, 2815, 3284, 3899, 4153, 4155, 4175, 4356, 4689, 4769, 4820, 4883, 5024, 5200, 5334, 5361, 5442, 5765, 5805, 5857, 6031, 6289, 6634, 6835, 7216, 7374, 7818, 8024, 8304, 9312}

R66 has these k remain for k<=10000:

{681, 1056, 1205, 1575, 1669, 1944, 2182, 2916, 2949, 3014, 3083, 3148, 3221, 3526, 3684, 3911, 3946, 4423, 5329, 5361, 5897, 5898, 5959, 5972, 6096, 6189, 6263, 6451, 6768, 6796, 7168, 7237, 7357, 7572, 7614, 7927, 8156, 8173, 8348, 8432, 8510, 8825, 8866, 9017, 9111, 9406, 9409, 9781, 9801, 9906, 9998}

S120 has these k remain for k<=10000:

{56, 89, 208, 219, 307, 309, 426, 540, 560, 694, 714, 727, 991, 1024, 1167, 1616, 1658, 1662, 1689, 1833, 1946, 1969, 1970, 2023, 2078, 2157, 2223, 2279, 2377, 2395, 2509, 2519, 2881, 3161, 3257, 3301, 3321, 3345, 3387, 3510, 3561, 3598, 3607, 3774, 3805, 3814, 3827, 3860, 3893, 3950, 4212, 4333, 4367, 4456, 4610, 4724, 4762, 4852, 4993, 5069, 5191, 5347, 5433, 5543, 5553, 5665, 5763, 5875, 5894, 5928, 6029, 6084, 6447, 6478, 6502, 6715, 6718, 6720, 6984, 7097, 7195, 7248, 7284, 7379, 7589, 7998, 8051, 8161, 8189, 8293, 8304, 8359, 8382, 8427, 8514, 8636, 8669, 8678, 8693, 8876, 8931, 8933, 8957, 9041, 9043, 9058, 9109, 9140, 9195, 9318, 9351, 9494, 9513, 9637, 9721, 9890}

R120 has these k remain for k<=10000:

{384, 386, 419, 483, 551, 672, 824, 846, 890, 901, 991, 1024, 1077, 1095, 1132, 1134, 1255, 1309, 1385, 1394, 1693, 1797, 1921, 2036, 2133, 2177, 2258, 2354, 2386, 2410, 2452, 2650, 2696, 2716, 3004, 3025, 3123, 3178, 3189, 3214, 3290, 3343, 3347, 3400, 3407, 3433, 3596, 3786, 3994, 4003, 4082, 4320, 4399, 4423, 4460, 4500, 4577, 4676, 4685, 4819, 4830, 4839, 4936, 5105, 5125, 5255, 5378, 5630, 5686, 5730, 6112, 6241, 6332, 6357, 6425, 6581, 6676, 6678, 6755, 6821, 6852, 6951, 6982, 6997, 7008, 7413, 7470, 7523, 7545, 7549, 7789, 7803, 7820, 7910, 7985, 8100, 8205, 8464, 8647, 8810, 8812, 8869, 8922, 8964, 8966, 8997, 9010, 9019, 9057, 9070, 9395, 9564, 9626, 9712, 9889, 9921, 9954, 9993}

S124 has these k remain for k<=10000:

{54, 61, 76, 83, 89, 96, 114, 121, 146, 171, 206, 209, 221, 239, 251, 344, 362, 376, 381, 386, 411, 416, 431, 446, 449, 516, 519, 526, 530, 576, 581, 601, 635, 646, 647, 656, 661, 669, 670, 676, 684, 731, 766, 794, 804, 809, 831, 836, 841, 872, 896, 911, 971, 976, 1019, 1031, 1051, 1054, 1076, 1111, 1124, 1129, 1136, 1166, 1190, 1229, 1251, 1254, 1259, 1264, 1284, 1298, 1324, 1326, 1336, 1369, 1421, 1446, 1460, 1461, 1471, 1474, 1477, 1499, 1519, 1535, 1536, 1551, 1569, 1586, 1591, 1601, 1604, 1647, 1657, 1676, 1686, 1700, 1721, 1727, 1734, 1741, 1779, 1801, 1814, 1829, 1844, 1864, 1910, 1955, 2021, 2034, 2036, 2045, 2055, 2067, 2069, 2096, 2097, 2109, 2114, 2129, 2159, 2163, 2179, 2216, 2234, 2266, 2306, 2316, 2354, 2374, 2375, 2406, 2414, 2429, 2436, 2446, 2462, 2504, 2507, 2539, 2559, 2561, 2565, 2621, 2639, 2646, 2651, 2716, 2726, 2734, 2799, 2821, 2834, 2840, 2844, 2861, 2864, 2874, 2901, 2906, 2934, 2981, 2999, 3019, 3032, 3041, 3049, 3053, 3071, 3144, 3161, 3164, 3181, 3229, 3236, 3242, 3251, 3281, 3285, 3296, 3299, 3316, 3329, 3351, 3405, 3442, 3470, 3471, 3491, 3494, 3533, 3554, 3561, 3574, 3631, 3659, 3674, 3684, 3714, 3726, 3736, 3737, 3758, 3779, 3806, 3824, 3854, 3869, 3881, 3890, 3911, 3916, 3921, 3941, 3961, 3981, 3986, 3994, 4021, 4049, 4086, 4089, 4124, 4127, 4131, 4153, 4162, 4191, 4196, 4226, 4231, 4254, 4297, 4306, 4314, 4352, 4375, 4388, 4406, 4414, 4421, 4454, 4476, 4489, 4500, 4506, 4520, 4521, 4529, 4541, 4546, 4589, 4594, 4604, 4629, 4719, 4739, 4751, 4764, 4769, 4799, 4849, 4891, 4910, 4926, 4936, 4952, 4961, 4964, 4973, 4974, 5001, 5041, 5048, 5049, 5108, 5114, 5121, 5149, 5154, 5189, 5191, 5231, 5244, 5279, 5289, 5300, 5316, 5321, 5326, 5364, 5366, 5369, 5375, 5381, 5384, 5414, 5440, 5462, 5474, 5481, 5489, 5519, 5543, 5551, 5579, 5581, 5596, 5651, 5663, 5681, 5696, 5697, 5701, 5721, 5723, 5738, 5744, 5771, 5781, 5799, 5801, 5816, 5819, 5825, 5839, 5840, 5851, 5876, 5884, 5909, 5919, 5939, 5951, 5976, 5981, 6024, 6026, 6036, 6041, 6046, 6059, 6099, 6146, 6151, 6161, 6164, 6166, 6196, 6201, 6211, 6219, 6224, 6241, 6269, 6296, 6310, 6323, 6329, 6366, 6383, 6386, 6394, 6401, 6409, 6410, 6411, 6416, 6486, 6494, 6496, 6511, 6514, 6536, 6539, 6559, 6596, 6620, 6621, 6644, 6646, 6647, 6654, 6659, 6665, 6686, 6689, 6691, 6696, 6712, 6729, 6731, 6746, 6749, 6751, 6761, 6789, 6794, 6806, 6821, 6864, 6881, 6891, 6904, 6908, 6926, 6949, 6956, 6959, 6962, 6971, 7004, 7006, 7016, 7034, 7036, 7071, 7074, 7079, 7081, 7146, 7169, 7204, 7216, 7227, 7239, 7259, 7269, 7271, 7276, 7301, 7319, 7324, 7331, 7359, 7369, 7376, 7391, 7424, 7439, 7446, 7451, 7454, 7472, 7484, 7486, 7499, 7523, 7544, 7559, 7564, 7565, 7586, 7601, 7609, 7639, 7656, 7664, 7666, 7671, 7691, 7739, 7744, 7761, 7796, 7801, 7831, 7851, 7868, 7881, 7886, 7931, 7949, 7979, 7981, 8014, 8017, 8034, 8042, 8054, 8114, 8141, 8146, 8192, 8213, 8219, 8221, 8231, 8274, 8279, 8291, 8296, 8321, 8323, 8351, 8354, 8381, 8396, 8417, 8423, 8424, 8429, 8516, 8519, 8526, 8531, 8532, 8579, 8634, 8641, 8651, 8666, 8681, 8711, 8714, 8741, 8771, 8776, 8780, 8786, 8829, 8831, 8876, 8916, 8921, 8930, 8936, 8939, 8966, 8978, 8982, 9006, 9024, 9026, 9038, 9069, 9099, 9106, 9118, 9138, 9161, 9166, 9173, 9187, 9209, 9214, 9216, 9226, 9244, 9261, 9267, 9269, 9286, 9302, 9314, 9319, 9411, 9424, 9479, 9483, 9509, 9521, 9536, 9594, 9596, 9598, 9599, 9641, 9651, 9681, 9687, 9743, 9754, 9785, 9791, 9831, 9836, 9865, 9866, 9901, 9911, 9914, 9949, 9971}

R124 has these k remain for k<=10000:

{101, 136, 146, 175, 179, 199, 204, 236, 259, 271, 301, 328, 364, 389, 434, 441, 459, 469, 561, 586, 589, 599, 604, 614, 616, 631, 661, 741, 766, 806, 844, 894, 901, 922, 931, 951, 971, 974, 1013, 1016, 1019, 1021, 1039, 1043, 1046, 1061, 1081, 1114, 1123, 1149, 1156, 1186, 1229, 1231, 1237, 1246, 1249, 1269, 1288, 1336, 1375, 1376, 1384, 1399, 1461, 1496, 1498, 1499, 1509, 1511, 1519, 1522, 1542, 1636, 1654, 1664, 1711, 1719, 1724, 1731, 1741, 1743, 1754, 1766, 1779, 1783, 1784, 1789, 1814, 1824, 1834, 1861, 1904, 1924, 1926, 1931, 1941, 1954, 1969, 1989, 2029, 2041, 2095, 2101, 2109, 2124, 2131, 2161, 2166, 2191, 2194, 2212, 2296, 2306, 2307, 2344, 2364, 2366, 2377, 2416, 2419, 2436, 2479, 2491, 2497, 2529, 2539, 2559, 2572, 2576, 2616, 2656, 2661, 2664, 2666, 2680, 2686, 2731, 2761, 2789, 2804, 2830, 2854, 2864, 2920, 2931, 2971, 2994, 3024, 3034, 3054, 3067, 3076, 3079, 3081, 3096, 3154, 3196, 3214, 3229, 3247, 3261, 3286, 3294, 3316, 3319, 3324, 3329, 3346, 3382, 3421, 3439, 3579, 3604, 3606, 3646, 3649, 3654, 3679, 3704, 3716, 3730, 3734, 3739, 3752, 3771, 3779, 3786, 3789, 3809, 3821, 3829, 3839, 3866, 3942, 3949, 3964, 3986, 4006, 4015, 4039, 4054, 4066, 4084, 4089, 4091, 4094, 4096, 4129, 4134, 4153, 4207, 4229, 4231, 4234, 4236, 4311, 4319, 4331, 4375, 4376, 4384, 4424, 4429, 4476, 4486, 4506, 4512, 4526, 4546, 4554, 4609, 4646, 4651, 4684, 4714, 4716, 4771, 4786, 4796, 4801, 4811, 4816, 4831, 4854, 4879, 4885, 4909, 4911, 4946, 4961, 4976, 4997, 5009, 5020, 5026, 5032, 5049, 5101, 5116, 5149, 5152, 5164, 5186, 5209, 5224, 5226, 5246, 5269, 5274, 5283, 5314, 5334, 5396, 5404, 5416, 5431, 5459, 5499, 5526, 5539, 5554, 5611, 5626, 5630, 5632, 5679, 5684, 5696, 5699, 5710, 5746, 5751, 5764, 5784, 5830, 5840, 5844, 5911, 5926, 5934, 5946, 5956, 5959, 5974, 5979, 5982, 6000, 6019, 6024, 6049, 6094, 6098, 6106, 6154, 6181, 6184, 6186, 6187, 6189, 6191, 6212, 6214, 6223, 6226, 6246, 6251, 6261, 6309, 6318, 6336, 6361, 6374, 6376, 6381, 6384, 6424, 6434, 6439, 6449, 6466, 6469, 6506, 6514, 6571, 6589, 6625, 6644, 6759, 6799, 6826, 6849, 6856, 6886, 6901, 6919, 6931, 6961, 6971, 6976, 6986, 7006, 7051, 7062, 7066, 7092, 7096, 7104, 7114, 7134, 7144, 7146, 7195, 7221, 7232, 7261, 7274, 7276, 7284, 7301, 7309, 7311, 7329, 7369, 7389, 7396, 7423, 7453, 7456, 7478, 7479, 7494, 7516, 7521, 7522, 7523, 7544, 7551, 7591, 7600, 7616, 7617, 7619, 7674, 7682, 7714, 7739, 7741, 7756, 7762, 7771, 7779, 7801, 7811, 7861, 7884, 7885, 7897, 7909, 7951, 8006, 8041, 8044, 8046, 8111, 8124, 8129, 8137, 8146, 8149, 8161, 8166, 8201, 8203, 8231, 8248, 8249, 8250, 8266, 8286, 8326, 8334, 8339, 8361, 8369, 8383, 8394, 8419, 8429, 8431, 8441, 8454, 8461, 8476, 8479, 8491, 8499, 8524, 8529, 8536, 8551, 8564, 8581, 8606, 8641, 8655, 8674, 8683, 8691, 8719, 8724, 8730, 8779, 8794, 8809, 8811, 8839, 8849, 8854, 8869, 8871, 8934, 8936, 8974, 8979, 8980, 8986, 9001, 9034, 9064, 9069, 9076, 9115, 9136, 9142, 9166, 9172, 9175, 9178, 9199, 9236, 9244, 9247, 9256, 9260, 9264, 9276, 9314, 9334, 9336, 9344, 9349, 9366, 9382, 9401, 9436, 9454, 9459, 9463, 9496, 9516, 9524, 9526, 9551, 9562, 9564, 9571, 9574, 9586, 9634, 9646, 9661, 9728, 9739, 9761, 9799, 9826, 9831, 9844, 9907, 9909, 9931, 9966, 9976}

[QUOTE=sweety439;547582]S120 has these k remain for k<=10000:

{56, 89, 208, 219, 307, 309, 426, 540, 560, 694, 714, 727, 991, 1024, 1167, 1616, 1658, 1662, 1689, 1833, 1946, 1969, 1970, 2023, 2078, 2157, 2223, 2279, 2377, 2395, 2509, 2519, 2881, 3161, 3257, 3301, 3321, 3345, 3387, 3510, 3561, 3598, 3607, 3774, 3805, 3814, 3827, 3860, 3893, 3950, 4212, 4333, 4367, 4456, 4610, 4724, 4762, 4852, 4993, 5069, 5191, 5347, 5433, 5543, 5553, 5665, 5763, 5875, 5894, 5928, 6029, 6084, 6447, 6478, 6502, 6715, 6718, 6720, 6984, 7097, 7195, 7248, 7284, 7379, 7589, 7998, 8051, 8161, 8189, 8293, 8304, 8359, 8382, 8427, 8514, 8636, 8669, 8678, 8693, 8876, 8931, 8933, 8957, 9041, 9043, 9058, 9109, 9140, 9195, 9318, 9351, 9494, 9513, 9637, 9721, 9890}[/QUOTE]

These k are from the same family:

{56, 6720}

Thus S120 has these k remain for k<=10000:

{56, 89, 208, 219, 307, 309, 426, 540, 560, 694, 714, 727, 991, 1024, 1167, 1616, 1658, 1662, 1689, 1833, 1946, 1969, 1970, 2023, 2078, 2157, 2223, 2279, 2377, 2395, 2509, 2519, 2881, 3161, 3257, 3301, 3321, 3345, 3387, 3510, 3561, 3598, 3607, 3774, 3805, 3814, 3827, 3860, 3893, 3950, 4212, 4333, 4367, 4456, 4610, 4724, 4762, 4852, 4993, 5069, 5191, 5347, 5433, 5543, 5553, 5665, 5763, 5875, 5894, 5928, 6029, 6084, 6447, 6478, 6502, 6715, 6718, 6984, 7097, 7195, 7248, 7284, 7379, 7589, 7998, 8051, 8161, 8189, 8293, 8304, 8359, 8382, 8427, 8514, 8636, 8669, 8678, 8693, 8876, 8931, 8933, 8957, 9041, 9043, 9058, 9109, 9140, 9195, 9318, 9351, 9494, 9513, 9637, 9721, 9890}