[QUOTE=sweety439;547584]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}[/QUOTE]

These k are from the same family:

{54, 6696}
{61, 7564}
{76, 9424}

Thus 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, 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, 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, 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}

S126 has these k remain for k = 4 mod 5 and k<=30000:

{259, 1084, 1154, 5099, 5529, 6059, 8304, 8659, 8759, 8779, 8829, 9429, 9474, 9624, 11429, 12094, 12414, 12799, 13129, 13264, 13274, 13309, 14299, 15454, 18119, 18394, 18594, 19479, 19484, 19499, 19559, 19894, 20394, 20609, 20914, 21369, 21679, 21694, 21999, 24119, 24764, 25399, 25624, 25739, 26374, 27179, 27884, 28374, 28729}

R126 has these k remain for k = 1 mod 5 and k<=30000:

{406, 3566, 3631, 3721, 4416, 4436, 4596, 5081, 6026, 6041, 7876, 8061, 8256, 8336, 8836, 9166, 9606, 9651, 9936, 11366, 11696, 12416, 13006, 13016, 14831, 15366, 15596, 16636, 17351, 17436, 17826, 18001, 18571, 19686, 19996, 20216, 21306, 21316, 22031, 23466, 24001, 24176, 24706, 25106, 25886, 26326, 27296, 28791, 29001, 29551}

Update the newest file of [URL="https://docs.google.com/document/d/e/2PACX-1vSDAd399_aY-s-YBbzf3TnCezkAHNLFh-BFf1DdFp44FkVTUVSID_QSWHXS-dpQuyR3XzFy8hFQNuSZ/pub"]Sierpinski problems[/URL] to include S66, S120, S124, and S126

[QUOTE=sweety439;547683]Update the newest file of [URL="https://docs.google.com/document/d/e/2PACX-1vSDAd399_aY-s-YBbzf3TnCezkAHNLFh-BFf1DdFp44FkVTUVSID_QSWHXS-dpQuyR3XzFy8hFQNuSZ/pub"]Sierpinski problems[/URL] to include S66, S120, S124, and S126[/QUOTE]

Fixed:

[URL="https://docs.google.com/document/d/e/2PACX-1vTdtMdx11M-nYXR2dSZ9ciCgKT0UWCXjWAyZW641nqOOeIsCL22zbJYDCwxf3V0Jjwc2GQC32hZJNKH/pub"]https://docs.google.com/document/d/e/2PACX-1vTdtMdx11M-nYXR2dSZ9ciCgKT0UWCXjWAyZW641nqOOeIsCL22zbJYDCwxf3V0Jjwc2GQC32hZJNKH/pub[/URL]

* There was not a space between "4" and "mod 5", but it should be.
* Missing k = 15876 for the remain k for S126.
* Fixed the size of the exponent (n).

[QUOTE=sweety439;547685]Fixed:

[URL="https://docs.google.com/document/d/e/2PACX-1vTdtMdx11M-nYXR2dSZ9ciCgKT0UWCXjWAyZW641nqOOeIsCL22zbJYDCwxf3V0Jjwc2GQC32hZJNKH/pub"]https://docs.google.com/document/d/e/2PACX-1vTdtMdx11M-nYXR2dSZ9ciCgKT0UWCXjWAyZW641nqOOeIsCL22zbJYDCwxf3V0Jjwc2GQC32hZJNKH/pub[/URL]

* There was not a space between "4" and "mod 5", but it should be.
* Missing k = 15876 for the remain k for S126.
* Fixed the size of the exponent (n).[/QUOTE]

Corrected the test limit of k for S126, it should be 30K, not 10K

[URL="https://docs.google.com/document/d/e/2PACX-1vSgeV6mlCZM5TDVoYApBC9e5dLM_7CFXEcX8eRawNIMAdKCvaINNNImReL81OQpnkh-p_kA8eJrDbW5/pub"]https://docs.google.com/document/d/e/2PACX-1vSgeV6mlCZM5TDVoYApBC9e5dLM_7CFXEcX8eRawNIMAdKCvaINNNImReL81OQpnkh-p_kA8eJrDbW5/pub[/URL]

Update newest file of [URL="https://docs.google.com/document/d/e/2PACX-1vRy1KFyq088ZaVjH9Crf9TBmYCUGsrRKfq8HDZJ69qfX5kzAM2aBv8Bc1r5XOKcCMdMRmfo3dswk_kQ/pub"]Riesel conjectures[/URL] to include R66, R120, R124, and R126

[URL="https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures"]https://github.com/xayahrainie4793/Extended-Sierpinski-Riesel-conjectures[/URL]

[URL="https://github.com/xayahrainie4793/the-1st-2nd-3rd-conjectures-of-the-extended-Sierpinski-Riesel-conjectures"]https://github.com/xayahrainie4793/the-1st-2nd-3rd-conjectures-of-the-extended-Sierpinski-Riesel-conjectures[/URL]

Corrected the size of the text

[URL="https://docs.google.com/document/d/e/2PACX-1vS4HB4317HOCi4bqTH-5QdsHuocQOw2w74T8y2Vv7KvAPDyscMme22BsaYO992E-B51tqIfKEMNJ-NW/pub"]Sierpinski problems[/URL]

[URL="https://docs.google.com/document/d/e/2PACX-1vQnUYL98ahNp4D8i0A4MuqvJW7q0hFL7b7BBQFM1MsrPVJGkLkO0GUjrry85FlMK-lza_A2E9yPx5GX/pub"]Riesel problems[/URL]

the "remain k" column of R126 lists "(not testing done)" because the R126 conjecture in CRUS lists "15231 k's remaining at n=2.5K; to be shown later." (CRUS does not show the remain k for R126), and I only tested the k not in CRUS, thus I do not have the list of the remain k for R126

[URL="https://docs.google.com/document/d/e/2PACX-1vTU3PR5EKMbYxPHaSuAmg4TvzoHAcqLsjaSebcpOBYQ1E0bhtzI191OgAwXYXqVcFbCMR31cy0Gs5Te/pub"]Sierpinski problems[/URL]

[URL="https://docs.google.com/document/d/e/2PACX-1vQSfWUMUMXA47_TyBey0pBxMRFnhJN-ExR1JwQMAob208FNXoD-oaAaApuX6cHlMPd3MZS-qU5gDtcD/pub"]Riesel problems[/URL]