Consider r = c x 10

^{n} 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 10

^{8}< r < 10

^{9}. And find the nearest prime exponent to r. Or r = c x 10

^{n} 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 ~ 10

^{8} sqrt (2) <

141421387 (factored)

147576139 (factored) < 147576140 ~10

^{8} 2^(1/e

^{gamma}) <

147576181 (factored)

157079621 (PRP C & cert) < 157079632.7 ~ 10

^{8} pi/2 <

157079633 (factored)

161803393 (factored) < 161803399 ~10

^{8} golden ratio <

161803403 (PRP C & cert)

(all listed above <50Mdigits are completed)

173205079 (PRP C & cert) < 173205081 ~ 10

^{8} sqrt (3) <

173205089 (factored)

223606793 (PRP in progress) < 223606798 ~ 10

^{8} sqrt (5) <

223606807 (PRP in progress)

271828171 (PRP in progress) < 271828183 ~10

^{8} e <

271828199 (PRP C & cert)

292005097 (factored) < 292005098 ~ 10

^{8} "

Buenos Aires constant" <

292005113 (PRP in progress)

314159257 (LL assignment stagnant; PRP in progress) < 314159265 ~10

^{8} pi <

314159311 (factored)

316227731 (factored) < 316227766 ~ 10

^{8} 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 10

^{8} e <

543656371 (TF, P-1 done, PRP in progress)

628318517 (TF & P-1 done) < 628318531 ~2 x 10

^{8} 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 ~ 10

^{9} pi/4 <

785398169 (factored)

853973387 (factored) < 853973422 ~ 10

^{8} e pi <

853973437 (TF, P-1 done)

942477787 (factored) < 942477796 ~3 x 10

^{8} pi <

942477799 (TF done, P-1 done)

986960431 (factored) < 986960440 ~10

^{8} pi

^{2} <

986960461 (TF & P-1 done)

Suggestions for additions to the above list are welcome by PM.

Top of reference tree:

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