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Old 2007-03-31, 07:33   #1
robert44444uk
 
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Jun 2003
Oxford, UK

1,901 Posts
Default Very high weight k

I generated some E52 Payam Numbers and then ran the first 30,000 or so through the Nash program, and for k < 2*10^18 the best results were:

1540289647689526305 8321 8325
104638339734650865 8336 8323
553356619963699695 8282 8293
372349639969432125 8279 8282
303443427206348715 8296 8281
596126609590333965 8262 8269
211795368487356225 8261 8269
893386008747621675 8258 8255
541726696764825 8247 8245
319257076933318095 8221 8238
1207387684290870225 8237 8231
545866456597997535 8241 8231
1824593579944198635 8229 8228
1793052151130579625 8213 8221
1562451592176289815 8229 8221
264767258358587985 8226 8218
199103567327900235 8208 8210
1227114671166403305 8202 8207
810216647861986365 8196 8206
1743046040807216145 8191 8205
578295298798646715 8207 8203

These are some of the highest Nash weights I have come across, however this does not necessarily imply a lot of primes.

I ran 3 of the above up to n=10000 and my results were:

104638339734650865 67 primes
553356619963699695 84 primes
541726696764825 66 primes

A good Payam E(52) number has 100 primes in the first 4000 n.

Regards

Robert Smith
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