Primes of both forms 24n+7 and 7m+24

Artur grafix at csl.pl
Thu Apr 24 10:00:09 CEST 2008


Dear Brendan,

>>Why is it interesting?

Because we never imagine when yet this same sequence can occured in 
another applications. ONEIS is Encyclopedia and will be good stored each 
of them (independent that some people treated this or other as less or 
more interesting for hisself)

Best wishes
Artur



Brendan McKay pisze:
> * zak seidov <zakseidov at yahoo.com> [080424 17:34]:
>   
>> A1 Primes of the both forms 24n+7 and 7m+24
>>     
>
> But that is the same thing as 168k+31.  Why is it interesting?
>
> Brendan.
>
>   
>> 31,199,367,1039,1543,1879,2383,2551,2719,2887,3391,3559,3727,4231,4567,4903,5407,5743,6079,6247,7591,7759,7927,8263,8431,8599,9103,9439,10111,11119,11287,11959,12799,12967,13807,14143,14479,14983,15319,15823,15991,16831,17167,17839,18679,19183,19687,20023,20359,21031,21871,22039,22543,23719,23887,24223,24391
>>
>> A2 Corresponding values of n
>> 1,8,15,43,64,78,99,106,113,120,141,148,155,176,190,204,225,239,253,260,316,323,330,344,351,358,379,393,421,463,470,498,533,540,575,589,603,624,638,659,666,701,715,743,778,799,820,834,848,876,911,918,939,988,995,1009,1016,1079,1100,1149,1156,1163,1170,1191,1198,1205,1233,1254,1261,1338,1415,1429,1436,1450,1471,1499
>>
>> A3 Corresponding values of m
>> 1,25,49,145,217,265,337,361,385,409,481,505,529,601,649,697,769,817,865,889,1081,1105,1129,1177,1201,1225,1297,1345,1441,1585,1609,1705,1825,1849,1969,2017,2065,2137,2185,2257,2281,2401,2449,2545,2665,2737,2809,2857,2905,3001,3121,3145,3217,3385,3409,3457,3481,3697,3769,3937,3961,3985,4009,4081,4105,4129,4225
>>
>> Difference between m and n is always multiple of 17
>> and 
>>
>> A4 Corresponding values of (m-n)/17
>> 0,1,2,6,9,11,14,15,16,17,20,21,22,25,27,29,32,34,36,37,45,46,47,49,50,51,54,56,60,66,67,71,76,77,82,84,86,89,91,94,95,100,102,106,111,114,117,119,121,125,130,131,134,141,142,144,145,154,157,164,165,166,167,170,171,172,176,179,180,191,202,204,205,207,210,214,215,216,221,224,225,227,230,231,234,235,236,237,240,241,244,249,254,257,259,
>>
>> Also all primes in A1 are of form 8k-1,
>> hence
>>
>> A5 Corresponding values of k
>>
>> 4,25,46,130,193,235,298,319,340,361,424,445,466,529,571,613,676,718,760,781,949,970,991,1033,1054,1075,1138,1180,1264,1390,1411,1495,1600,1621,1726,1768,1810,1873,1915,1978,1999,2104,2146,2230,2335,2398,2461,2503,2545,2629,2734,2755,2818,2965,2986,3028,3049,3238,3301,3448,3469,3490,3511,3574,3595,3616,3700
>>
>> Are there any other (interesting) properties of
>> primes in A1?
>> thanks, zak
>>  
>>
>>
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>
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