[kriesel]

Consider r = c x 10ⁿ x b, where b is an irrational number such as pi, e, sqrt(2), sqrt(3), sqrt(5), sqrt(10), etc and where c, n are are small positive integers chosen such that 10⁸< r < 10⁹. And find the nearest prime exponent to r. Or r = c x 10ⁿ x b^m where b is a transcendental number and m is also a small positive integer.

Factoring or primality testing on such exponents may be useful by falling in regions of the number line that would not be selected otherwise in a simple QA selection method.

Some early examples of such runs revealed limitations on CUDAPm1 exponent that were later found to be partly gpu-model dependent.
141421333 (PRP C & cert) < 141421356 ~ 10⁸ sqrt (2) < 141421387 (factored)
147576139 (factored) < 147576140 ~10⁸ 2^(1/e^gamma) < 147576181 (factored)
157079621 (PRP C & cert) < 157079632.7 ~ 10⁸ pi/2 < 157079633 (factored)
161803393 (factored) < 161803399 ~10⁸ golden ratio < 161803403 (PRP C & cert)
(all listed above <50Mdigits are completed)
173205079 (PRP C & cert) < 173205081 ~ 10⁸ sqrt (3) < 173205089 (factored)
223606793 (PRP in progress) < 223606798 ~ 10⁸ sqrt (5) < 223606807 (PRP in progress)
271828171 (PRP in progress) < 271828183 ~10⁸ e < 271828199 (PRP C & cert)
292005097 (factored) < 292005098 ~ 10⁸ "Buenos Aires constant" < 292005113 (PRP in progress)
314159257 (LL assignment stagnant; PRP in progress) < 314159265 ~10⁸ pi < 314159311 (factored)
316227731 (factored) < 316227766 ~ 10⁸ sqrt(10) < 316227767 (factored)
(As of 2021-04-16, all listed above that are >50Mdigits & <100Mdigits are factored, or completed in TF and P-1 to recommended bit levels and bounds and primality tests are in progress)
543656363 (factored) < 543656366 ~2 x 10⁸ e < 543656371 (TF, P-1 done, PRP in progress)
628318517 (TF & P-1 done) < 628318531 ~2 x 10⁸ pi < 628318583 (TF & P-1 done)
(As of 2021-04-16, all listed above that are >100Mdigits & <200Mdigits are factored, or completed in TF and P-1 to recommended bit levels and bounds)
(As of 2021-02-27, all listed below >200Mdigits are factored, or TF completed to recommended bit levels and P-1 done to at least recommended bounds)
785398129 (factored) < 785398163 ~ 10⁹ pi/4 < 785398169 (factored)
853973387 (factored) < 853973422 ~ 10⁸ e pi < 853973437 (TF, P-1 done)
942477787 (factored) < 942477796 ~3 x 10⁸ pi < 942477799 (TF done, P-1 done)
986960431 (factored) < 986960440 ~10⁸ pi² < 986960461 (TF & P-1 done)
Suggestions for additions to the above list are welcome by PM.


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