files / problems / two-smooth-summands / compute / certs / obstruction.json
{
"M_star": 131486759,
"A045535_prefix_check": [
{
"n": 0,
"m": 7,
"y": 2,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 1,
"m": 23,
"y": 3,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 2,
"m": 71,
"y": 5,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 3,
"m": 311,
"y": 7,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 4,
"m": 479,
"y": 11,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 5,
"m": 1559,
"y": 13,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 6,
"m": 5711,
"y": 17,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 7,
"m": 10559,
"y": 19,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 8,
"m": 18191,
"y": 23,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 9,
"m": 31391,
"y": 29,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 10,
"m": 118271,
"y": 31,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 11,
"m": 366791,
"y": 37,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 12,
"m": 366791,
"y": 41,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 13,
"m": 2155919,
"y": 43,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 14,
"m": 2155919,
"y": 47,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 15,
"m": 2155919,
"y": 53,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 16,
"m": 6077111,
"y": 59,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 17,
"m": 6077111,
"y": 61,
"ok": true,
"smaller": null,
"leastness_checked": true
},
{
"n": 18,
"m": 98538359,
"y": 67,
"ok": true,
"smaller": null,
"leastness_checked": false
},
{
"n": 19,
"m": 120293879,
"y": 71,
"ok": true,
"smaller": null,
"leastness_checked": false
},
{
"n": 20,
"m": 131486759,
"y": 73,
"ok": true,
"smaller": null,
"leastness_checked": false
},
{
"n": 21,
"m": 131486759,
"y": 79,
"ok": true,
"smaller": null,
"leastness_checked": false
},
{
"n": 22,
"m": 508095719,
"y": 83,
"ok": true,
"smaller": null,
"leastness_checked": false
}
],
"A045535_prefix_failures": [],
"roots_M_star": [
{
"q": 3,
"r": 1,
"ok": true
},
{
"q": 5,
"r": 1,
"ok": true
},
{
"q": 7,
"r": 3,
"ok": true
},
{
"q": 11,
"r": 5,
"ok": true
},
{
"q": 13,
"r": 5,
"ok": true
},
{
"q": 17,
"r": 8,
"ok": true
},
{
"q": 19,
"r": 9,
"ok": true
},
{
"q": 23,
"r": 3,
"ok": true
},
{
"q": 29,
"r": 13,
"ok": true
},
{
"q": 31,
"r": 12,
"ok": true
},
{
"q": 37,
"r": 17,
"ok": true
},
{
"q": 41,
"r": 6,
"ok": true
},
{
"q": 43,
"r": 19,
"ok": true
},
{
"q": 47,
"r": 21,
"ok": true
},
{
"q": 53,
"r": 26,
"ok": true
},
{
"q": 59,
"r": 13,
"ok": true
},
{
"q": 61,
"r": 12,
"ok": true
},
{
"q": 67,
"r": 2,
"ok": true
},
{
"q": 71,
"r": 22,
"ok": true
},
{
"q": 73,
"r": 29,
"ok": true
},
{
"q": 79,
"r": 29,
"ok": true
}
],
"roots_failures": [],
"lemma_small_m": [
{
"m": 7,
"y": 2,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 23,
"y": 3,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 71,
"y": 5,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 311,
"y": 7,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 479,
"y": 11,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 1559,
"y": 13,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 5711,
"y": 17,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 10559,
"y": 19,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 18191,
"y": 23,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 31391,
"y": 29,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 118271,
"y": 31,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 366791,
"y": 37,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 366791,
"y": 41,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 2155919,
"y": 43,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 2155919,
"y": 47,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 2155919,
"y": 53,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 6077111,
"y": 59,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
},
{
"m": 6077111,
"y": 61,
"is_neg_pseudosquare": true,
"representation": null,
"blocked_as_predicted": true
}
],
"lemma_small_failures": [],
"F_M_star": {
"value": 83,
"split": [
649,
131486110
],
"factors_a": [
11,
59
],
"factors_b": [
2,
5,
7,
7,
53,
61,
83
],
"P_a": 59,
"P_b": 83,
"neg_pseudosquare_through_79": true,
"has_79_smooth_split": false,
"no_prime_between_79_and_83": true,
"conclusion": true
},
"smooth_counts_through_M_star": {
"y73": 727473,
"y79": 808372
},
"is_dent": false,
"reason": "Exact pointwise F and the reciprocity obstruction; not an exponent."
}