- djbroadhurst wrote:
> > Small supplement your results

Now your 20 numbers and numbers from

> > Pk -> n = 0..10^k

> >

> > {rank/P4,{a, P2, P4, P5, P6}}

> > {1,{247757,71,5028,39759,324001}}

> > {2,{595937,61,4978,39293,322141}}

> ....

> > {16,{15102077,46,4631,38561,318251}}

>

> Thanks, Marian. Note that what was in 16th place when

> ranked by P4 is now in third place when ranked by P6.

>

http://pages.cpsc.ucalgary.ca/~jacobs/PDF/mthesis.pdf page 114, a = (1-D)/4

and a = 41

Pk -> n = 0..10^k

{rank/P7,{a, P2, P3, P4, P5, P6, P7}}

{1,{18552607567337,37,323,3255,32450,323290,3155718}}

{2,{27646977664127,34,302,3195,32121,321488,3145878}}

{3,{9305398948667,25,335,3265,32494,325086,3129775}}

{4,{7514981191031,35,331,3230,32672,326392,3123122}}

{5,{21425625701,41,401,3971,39289,361841,3121627}}

{6,{132874279528931,33,307,3141,31149,312975,3107983}}

{7,{4125444938831,30,302,3266,32701,326605,3084227}}

{8,{17959429571,42,406,3898,38770,354875,3057636}}

{9,{517165153168577,24,282,3014,30179,300923,3004626}}

{10,{1016793977,44,430,4253,40452,346058,2945779}}

{11,{398878547,46,444,4277,40340,341572,2898571}}

{12,{160834691,47,451,4439,40065,335225,2840202}}

{13,{352031501,37,419,4312,39703,334712,2840132}}

{14,{99539591,52,445,4392,39096,325783,2763613}}

{15,{247757,71,657,5028,39759,324001,2742499}}

{16,{67374467,42,454,4420,38827,322489,2731742}}

{17,{595937,61,609,4978,39293,322141,2729508}}

{18,{42895751,50,474,4504,38815,320126,2713363}}

{19,{15102077,46,474,4631,38561,318251,2692395}}

{20,{2640161,61,533,4799,38501,315542,2670563}}

{21,{8930807,55,518,4676,38343,315433,2669432}}

{22,{1544987,59,559,4809,38361,314274,2660965}}

{23,{2367767,55,538,4767,38058,312437,2642693}}

{24,{3106001,46,521,4684,37831,310304,2624296}}

{25,{701147,62,563,4713,37376,305818,2587905}}

{26,{1974881,52,536,4644,37261,305096,2578908}}

{27,{765197,57,569,4666,36893,303389,2569941}}

{28,{239621,62,605,4724,36976,303476,2567792}}

{29,{115721,69,627,4691,37059,302999,2563493}}

{30,{361637,63,591,4634,36644,299939,2536717}}

{31,{333491,60,587,4669,36592,300002,2535781}}

{32,{722231,57,562,4610,36610,299667,2535210}}

{33,{771581,59,551,4670,36404,299303,2530509}}

{34,{3399714628553118047,24,235,2482,25034,251841,2517022}} !!

{35,{601037,57,551,4605,36308,297251,2513444}}

{36,{136517,66,611,4609,36230,297046,2512291}}

{37,{383681,63,571,4613,35863,294775,2494339}}

{38,{41,87,582,4149,31985,261081,2208197}}

--

marian otremba - --- In primenumbers@yahoogroups.com,

"WarrenS" <warren.wds@...> wrote:

> > Let N(a,n1,n2) be the number of primes of the form

Bad models.

> > n^2+n+a with n in [n1,n1+n2]. Then the data

> >

> > N(247757,0,10^6) = 324001

> > N(3399714628553118047,0,10^6) = 251841

> >

> > seem to favour the smaller value of a. Yet these data

> >

> > N(247757,10^12,10^6) = 148817

> > N(3399714628553118047,10^12,10^6) = 193947

> >

> > indicate that the larger value of a is better, in the long run.

>

> --these numbers seem to be in vast violation of naive statistical

> models.

> Is the reason, that the length n2 of the sampling interval,

No. Rather it is that n1, the begining of the sampling

> needs to be substantially larger than a, in order for naive

> statistical models to become reasonably valid?

interval, needs to be substantially larger than sqrt(a),

for the HL heuristic to win out. Clearly when

n1 < sqrt(3399714628553118047), Marion was comparing apples

and oranges, since log(n^2+n+a) was dominated by "a".

All I did was to level the playing field, here:

> N(247757,10^12,10^6) = 148817

to allow the HL heuristic to show through.

> N(3399714628553118047,10^12,10^6) = 193947

It's a simple as that. No shock-horror for statisticians;

Just a trivial observation by a log-lover :-)

David