When the index is prime or odd then the sum is always even but
when the index is even the sum is always odd and a 0(mod 3)
or an odd composite except for (6) exceptions in the first 14 indexs. ---
1)= 2 * = Exception.
2)= 5 *
3)= 10
4)= 17 *
5)= 28
6)= 41 *
7)= 58
8)= 77
9)= 100
10)= 129
11)= 160
12)= 197 *
13)= 238
14)= 281 *
15)= 328
16)= 381
17)= 440
18)= 501
19)= 568
20)= 639
21)= 712
22)= 791
23)= 874
24)= 963
25)= 1060
26)= 1161
27)= 1264
28)= 1371
29)= 1480
30)= 1593
31)= 1720
32)= 1851
33)= 1988
34)= 2127
35)= 2276
36)= 2427
...
Will, there ever be an even index where its sum is prime after
the last exception, index 14)and prime 281?

Dan

On Wednesday, May 12, 2021 at 1:47:04 PM UTC-7, djoyce099 wrote:
> When the index is prime or odd then the sum is always even but
> when the index is even the sum is always odd and a 0(mod 3)
> or an odd composite except for (6) exceptions in the first 14 indexs. ---
> 1)= 2 * = Exception.
> 2)= 5 *
> 3)= 10
> 4)= 17 *
> 5)= 28
> 6)= 41 *
> 7)= 58
> 8)= 77
> 9)= 100
> 10)= 129
> 11)= 160
> 12)= 197 *
> 13)= 238
> 14)= 281 *
> 15)= 328
> ..
> Will, there ever be an even index where its sum is prime after
> the last exception, index 14)and prime 281?
> Dan

Map[First,Select[Partition[FoldList[Plus,0,Select[Range[10^4],PrimeQ]],2],PrimeQ[#[[1]]]&]]

{5,17,41,197,281,7699,8893,22039,24133,25237,28697,32353,37561,38921,43201,44683,55837,61027,
66463,70241,86453,102001,109147,116533,119069,121631,129419,132059,263171,287137,325019,
329401,333821,338279,342761,360979,379667,393961,398771,581921,642869,681257,687767,700897,
754573,768373,782263,868151,935507,958577,1005551,1086557,1313041,1359329,1583293,1603597,
1686239,1749833,1891889,2051167,2086159,2133121,2156813,2180741,2327399,2364833,2402537,
2504323,2556187,2582401,2608699,3120833,3238237,3557303,3619807,3875933,3892271,3925069,
3974497,4260917,4504663,4682791,4846279,4901431,4956893,4975457,5238847,5353841,5373133,
5411839,5666783}

On Wed, 12 May 2021 14:13:39 -0700 (PDT), bwr fml <qbwrfmlx@gmail.com>
wrote:

>On Wednesday, May 12, 2021 at 1:47:04 PM UTC-7, djoyce099 wrote:
>> When the index is prime or odd then the sum is always even but
>> when the index is even the sum is always odd and a 0(mod 3)
>> or an odd composite except for (6) exceptions in the first 14 indexs. ---
>> 1)= 2 * = Exception.
>> 2)= 5 *
>> 3)= 10
>> 4)= 17 *
>> 5)= 28
>> 6)= 41 *
>> 7)= 58
>> 8)= 77
>> 9)= 100
>> 10)= 129
>> 11)= 160
>> 12)= 197 *
>> 13)= 238
>> 14)= 281 *
>> 15)= 328
>> ..
>> Will, there ever be an even index where its sum is prime after
>> the last exception, index 14)and prime 281?
>> Dan
>
>Map[First,Select[Partition[FoldList[Plus,0,Select[Range[10^4],PrimeQ]],2],PrimeQ[#[[1]]]&]]
>
>{5,17,41,197,281,7699,8893,22039,24133,25237,28697,32353,37561,38921,43201,44683,55837,61027,
>66463,70241,86453,102001,109147,116533,119069,121631,129419,132059,263171,287137,325019,
>329401,333821,338279,342761,360979,379667,393961,398771,581921,642869,681257,687767,700897,
>754573,768373,782263,868151,935507,958577,1005551,1086557,1313041,1359329,1583293,1603597,
>1686239,1749833,1891889,2051167,2086159,2133121,2156813,2180741,2327399,2364833,2402537,
>2504323,2556187,2582401,2608699,3120833,3238237,3557303,3619807,3875933,3892271,3925069,
>3974497,4260917,4504663,4682791,4846279,4901431,4956893,4975457,5238847,5353841,5373133,
>5411839,5666783}

These are the prime sums for primes less that 10,000. Here are the
136 results for the primes after 41 up to prime index 1950 (after
which the sum exceeds prime index 1000000).

For prime[14] which is 43, the sum is 281 which is prime[60].
For prime[60] which is 281, the sum is 7699 which is prime[977].
For prime[64] which is 311, the sum is 8893 which is prime[1108].
For prime[96] which is 503, the sum is 22039 which is prime[2470].
For prime[100] which is 541, the sum is 24133 which is prime[2687].
For prime[102] which is 557, the sum is 25237 which is prime[2784].
For prime[108] which is 593, the sum is 28697 which is prime[3126].
For prime[114] which is 619, the sum is 32353 which is prime[3470].
For prime[122] which is 673, the sum is 37561 which is prime[3977].
For prime[124] which is 683, the sum is 38921 which is prime[4100].
For prime[130] which is 733, the sum is 43201 which is prime[4511].
For prime[132] which is 743, the sum is 44683 which is prime[4644].
For prime[146] which is 839, the sum is 55837 which is prime[5668].
For prime[152] which is 881, the sum is 61027 which is prime[6148].
For prime[158] which is 929, the sum is 66463 which is prime[6627].
For prime[162] which is 953, the sum is 70241 which is prime[6963].
For prime[178] which is 1061, the sum is 86453 which is prime[8407].
For prime[192] which is 1163, the sum is 102001 which is prime[9767].
For prime[198] which is 1213, the sum is 109147 which is prime[10379].
For prime[204] which is 1249, the sum is 116533 which is prime[11007].
For prime[206] which is 1277, the sum is 119069 which is prime[11220].
For prime[208] which is 1283, the sum is 121631 which is prime[11449].
For prime[214] which is 1307, the sum is 129419 which is prime[12111].
For prime[216] which is 1321, the sum is 132059 which is prime[12332].
For prime[296] which is 1949, the sum is 263171 which is prime[23080].
For prime[308] which is 2029, the sum is 287137 which is prime[25001].
For prime[326] which is 2161, the sum is 325019 which is prime[28009].
For prime[328] which is 2203, the sum is 329401 which is prime[28357].
For prime[330] which is 2213, the sum is 333821 which is prime[28709].
For prime[332] which is 2237, the sum is 338279 which is prime[29060].
For prime[334] which is 2243, the sum is 342761 which is prime[29404].
For prime[342] which is 2297, the sum is 360979 which is prime[30824].
For prime[350] which is 2357, the sum is 379667 which is prime[32271].
For prime[356] which is 2393, the sum is 393961 which is prime[33397].
For prime[358] which is 2411, the sum is 398771 which is prime[33764].
For prime[426] which is 2957, the sum is 581921 which is prime[47735].
For prime[446] which is 3137, the sum is 642869 which is prime[52278].
For prime[458] which is 3251, the sum is 681257 which is prime[55159].
For prime[460] which is 3257, the sum is 687767 which is prime[55646].
For prime[464] which is 3301, the sum is 700897 which is prime[56611].
For prime[480] which is 3413, the sum is 754573 which is prime[60585].
For prime[484] which is 3461, the sum is 768373 which is prime[61615].
For prime[488] which is 3491, the sum is 782263 which is prime[62644].
For prime[512] which is 3671, the sum is 868151 which is prime[68954].
For prime[530] which is 3821, the sum is 935507 which is prime[73872].
For prime[536] which is 3863, the sum is 958577 which is prime[75519].
For prime[548] which is 3947, the sum is 1005551 which is
prime[78913].
For prime[568] which is 4129, the sum is 1086557 which is
prime[84746].
For prime[620] which is 4583, the sum is 1313041 which is
prime[100950].
For prime[630] which is 4657, the sum is 1359329 which is
prime[104212].
For prime[676] which is 5051, the sum is 1583293 which is
prime[119983].
For prime[680] which is 5087, the sum is 1603597 which is
prime[121402].
For prime[696] which is 5233, the sum is 1686239 which is
prime[127179].
For prime[708] which is 5351, the sum is 1749833 which is
prime[131596].
For prime[734] which is 5563, the sum is 1891889 which is
prime[141473].
For prime[762] which is 5807, the sum is 2051167 which is
prime[152464].
For prime[768] which is 5849, the sum is 2086159 which is
prime[154859].
For prime[776] which is 5897, the sum is 2133121 which is
prime[158093].
For prime[780] which is 5939, the sum is 2156813 which is
prime[159724].
For prime[784] which is 6007, the sum is 2180741 which is
prime[161372].
For prime[808] which is 6211, the sum is 2327399 which is
prime[171355].
For prime[814] which is 6263, the sum is 2364833 which is
prime[173900].
For prime[820] which is 6301, the sum is 2402537 which is
prime[176463].
For prime[836] which is 6427, the sum is 2504323 which is
prime[183363].
For prime[844] which is 6529, the sum is 2556187 which is
prime[186889].
For prime[848] which is 6563, the sum is 2582401 which is
prime[188690].
For prime[852] which is 6581, the sum is 2608699 which is
prime[190446].
For prime[926] which is 7243, the sum is 3120833 which is
prime[224901].
For prime[942] which is 7433, the sum is 3238237 which is
prime[232811].
For prime[984] which is 7757, the sum is 3557303 which is
prime[253898].
For prime[992] which is 7853, the sum is 3619807 which is
prime[258076].
For prime[1024] which is 8161, the sum is 3875933 which is
prime[275006].
For prime[1026] which is 8171, the sum is 3892271 which is
prime[276090].
For prime[1030] which is 8219, the sum is 3925069 which is
prime[278258].
For prime[1036] which is 8263, the sum is 3974497 which is
prime[281504].
For prime[1070] which is 8597, the sum is 4260917 which is
prime[300308].
For prime[1098] which is 8819, the sum is 4504663 which is
prime[316261].
For prime[1118] which is 9001, the sum is 4682791 which is
prime[327839].
For prime[1136] which is 9161, the sum is 4846279 which is
prime[338451].
For prime[1142] which is 9209, the sum is 4901431 which is
prime[342101].
For prime[1148] which is 9277, the sum is 4956893 which is
prime[345691].
For prime[1150] which is 9283, the sum is 4975457 which is
prime[346897].
For prime[1178] which is 9511, the sum is 5238847 which is
prime[363935].
For prime[1190] which is 9631, the sum is 5353841 which is
prime[371372].
For prime[1192] which is 9649, the sum is 5373133 which is
prime[372606].
For prime[1196] which is 9689, the sum is 5411839 which is
prime[375120].
For prime[1222] which is 9907, the sum is 5666783 which is
prime[391452].
For prime[1240] which is 10099, the sum is 5847047 which is
prime[403009].
For prime[1256] which is 10247, the sum is 6009791 which is
prime[413494].
For prime[1296] which is 10627, the sum is 6426919 which is
prime[440130].
For prime[1314] which is 10789, the sum is 6619643 which is
prime[452439].
For prime[1322] which is 10867, the sum is 6706397 which is
prime[457914].
For prime[1338] which is 11047, the sum is 6881663 which is
prime[469115].
For prime[1356] which is 11197, the sum is 7081849 which is
prime[481857].
For prime[1386] which is 11491, the sum is 7422539 which is
prime[503392].
For prime[1394] which is 11587, the sum is 7514851 which is
prime[509187].
For prime[1400] which is 11657, the sum is 7584569 which is
prime[513573].
For prime[1408] which is 11731, the sum is 7678183 which is
prime[519514].
For prime[1418] which is 11827, the sum is 7796123 which is
prime[526907].
For prime[1420] which is 11833, the sum is 7819787 which is
prime[528412].
For prime[1446] which is 12073, the sum is 8130767 which is
prime[547965].
For prime[1460] which is 12211, the sum is 8300797 which is
prime[558652].
For prime[1466] which is 12263, the sum is 8374271 which is
prime[563255].
For prime[1474] which is 12343, the sum is 8472683 which is
prime[569380].
For prime[1476] which is 12373, the sum is 8497403 which is
prime[570967].
For prime[1478] which is 12379, the sum is 8522159 which is
prime[572524].
For prime[1494] which is 12511, the sum is 8721413 which is
prime[585077].
For prime[1500] which is 12553, the sum is 8796637 which is
prime[589800].
For prime[1502] which is 12577, the sum is 8821783 which is
prime[591345].
For prime[1510] which is 12641, the sum is 8922677 which is
prime[597642].
For prime[1524] which is 12781, the sum is 9100613 which is
prime[608710].
For prime[1526] which is 12799, the sum is 9126203 which is
prime[610285].
For prime[1546] which is 12979, the sum is 9384209 which is
prime[626420].
For prime[1606] which is 13577, the sum is 10180459 which is
prime[675795].
For prime[1630] which is 13781, the sum is 10508989 which is
prime[696179].
For prime[1632] which is 13799, the sum is 10536577 which is
prime[697857].
For prime[1638] which is 13873, the sum is 10619617 which is
prime[702978].
For prime[1664] which is 14143, the sum is 10983353 which is
prime[725501].
For prime[1690] which is 14419, the sum is 11354851 which is
prime[748373].
For prime[1726] which is 14741, the sum is 11879939 which is
prime[780681].
For prime[1746] which is 14897, the sum is 12176371 which is
prime[798853].
For prime[1752] which is 14957, the sum is 12266017 which is
prime[804333].
For prime[1762] which is 15083, the sum is 12416377 which is
prime[813624].
For prime[1766] which is 15121, the sum is 12476797 which is
prime[817306].
For prime[1770] which is 15149, the sum is 12537353 which is
prime[820978].
For prime[1774] which is 15193, the sum is 12598067 which is
prime[824683].
For prime[1784] which is 15277, the sum is 12750523 which is
prime[834058].
For prime[1842] which is 15791, the sum is 13651669 which is
prime[888866].
For prime[1844] which is 15803, the sum is 13683269 which is
prime[890827].
For prime[1888] which is 16249, the sum is 14388733 which is
prime[933747].
For prime[1912] which is 16493, the sum is 14782039 which is
prime[957585].
For prime[1916] which is 16553, the sum is 14848187 which is
prime[961590].
For prime[1922] which is 16619, the sum is 14947717 which is
prime[967573].
For prime[1944] which is 16843, the sum is 15315721 which is
prime[989804].
For prime[1948] which is 16889, the sum is 15383243 which is
prime[993852].
For prime[1950] which is 16903, the sum is 15417047 which is
prime[995857].

On Wednesday, May 12, 2021 at 7:35:22 PM UTC-4, Barry Schwarz wrote:
> On Wed, 12 May 2021 14:13:39 -0700 (PDT), bwr fml <qbwr...@gmail.com>
> wrote:
> >On Wednesday, May 12, 2021 at 1:47:04 PM UTC-7, djoyce099 wrote:
> >> When the index is prime or odd then the sum is always even but
> >> when the index is even the sum is always odd and a 0(mod 3)
> >> or an odd composite except for (6) exceptions in the first 14 indexs. ---
> >> 1)= 2 * = Exception.
> >> 2)= 5 *
> >> 3)= 10
> >> 4)= 17 *
> >> 5)= 28
> >> 6)= 41 *
> >> 7)= 58
> >> 8)= 77
> >> 9)= 100
> >> 10)= 129
> >> 11)= 160
> >> 12)= 197 *
> >> 13)= 238
> >> 14)= 281 *
> >> 15)= 328
> >> ..
> >> Will, there ever be an even index where its sum is prime after
> >> the last exception, index 14)and prime 281?
> >> Dan
> >
> >Map[First,Select[Partition[FoldList[Plus,0,Select[Range[10^4],PrimeQ]],2],PrimeQ[#[[1]]]&]]
> >
> >{5,17,41,197,281,7699,8893,22039,24133,25237,28697,32353,37561,38921,43201,44683,55837,61027,
> >66463,70241,86453,102001,109147,116533,119069,121631,129419,132059,263171,287137,325019,
> >329401,333821,338279,342761,360979,379667,393961,398771,581921,642869,681257,687767,700897,
> >754573,768373,782263,868151,935507,958577,1005551,1086557,1313041,1359329,1583293,1603597,
> >1686239,1749833,1891889,2051167,2086159,2133121,2156813,2180741,2327399,2364833,2402537,
> >2504323,2556187,2582401,2608699,3120833,3238237,3557303,3619807,3875933,3892271,3925069,
> >3974497,4260917,4504663,4682791,4846279,4901431,4956893,4975457,5238847,5353841,5373133,
> >5411839,5666783}
> These are the prime sums for primes less that 10,000. Here are the
> 136 results for the primes after 41 up to prime index 1950 (after
> which the sum exceeds prime index 1000000).
>
> For prime[14] which is 43, the sum is 281 which is prime[60].
> For prime[60] which is 281, the sum is 7699 which is prime[977].
> For prime[64] which is 311, the sum is 8893 which is prime[1108].
> For prime[96] which is 503, the sum is 22039 which is prime[2470].
> For prime[100] which is 541, the sum is 24133 which is prime[2687].
> For prime[102] which is 557, the sum is 25237 which is prime[2784].
> For prime[108] which is 593, the sum is 28697 which is prime[3126].
> For prime[114] which is 619, the sum is 32353 which is prime[3470].
> For prime[122] which is 673, the sum is 37561 which is prime[3977].
> For prime[124] which is 683, the sum is 38921 which is prime[4100].
> For prime[130] which is 733, the sum is 43201 which is prime[4511].
> For prime[132] which is 743, the sum is 44683 which is prime[4644].
> For prime[146] which is 839, the sum is 55837 which is prime[5668].
> For prime[152] which is 881, the sum is 61027 which is prime[6148].
> For prime[158] which is 929, the sum is 66463 which is prime[6627].
> For prime[162] which is 953, the sum is 70241 which is prime[6963].
> For prime[178] which is 1061, the sum is 86453 which is prime[8407].
> For prime[192] which is 1163, the sum is 102001 which is prime[9767].
> For prime[198] which is 1213, the sum is 109147 which is prime[10379].
> For prime[204] which is 1249, the sum is 116533 which is prime[11007].
> For prime[206] which is 1277, the sum is 119069 which is prime[11220].
> For prime[208] which is 1283, the sum is 121631 which is prime[11449].
> For prime[214] which is 1307, the sum is 129419 which is prime[12111].
> For prime[216] which is 1321, the sum is 132059 which is prime[12332].
> For prime[296] which is 1949, the sum is 263171 which is prime[23080].
> For prime[308] which is 2029, the sum is 287137 which is prime[25001].
> For prime[326] which is 2161, the sum is 325019 which is prime[28009].
> For prime[328] which is 2203, the sum is 329401 which is prime[28357].
> For prime[330] which is 2213, the sum is 333821 which is prime[28709].
> For prime[332] which is 2237, the sum is 338279 which is prime[29060].
> For prime[334] which is 2243, the sum is 342761 which is prime[29404].
> For prime[342] which is 2297, the sum is 360979 which is prime[30824].
> For prime[350] which is 2357, the sum is 379667 which is prime[32271].
> For prime[356] which is 2393, the sum is 393961 which is prime[33397].
> For prime[358] which is 2411, the sum is 398771 which is prime[33764].
> For prime[426] which is 2957, the sum is 581921 which is prime[47735].
> For prime[446] which is 3137, the sum is 642869 which is prime[52278].
> For prime[458] which is 3251, the sum is 681257 which is prime[55159].
> For prime[460] which is 3257, the sum is 687767 which is prime[55646].
> For prime[464] which is 3301, the sum is 700897 which is prime[56611].
> For prime[480] which is 3413, the sum is 754573 which is prime[60585].
> For prime[484] which is 3461, the sum is 768373 which is prime[61615].
> For prime[488] which is 3491, the sum is 782263 which is prime[62644].
> For prime[512] which is 3671, the sum is 868151 which is prime[68954].
> For prime[530] which is 3821, the sum is 935507 which is prime[73872].
> For prime[536] which is 3863, the sum is 958577 which is prime[75519].
> For prime[548] which is 3947, the sum is 1005551 which is
> prime[78913].
> For prime[568] which is 4129, the sum is 1086557 which is
> prime[84746].
> For prime[620] which is 4583, the sum is 1313041 which is
> prime[100950].
> For prime[630] which is 4657, the sum is 1359329 which is
> prime[104212].
> For prime[676] which is 5051, the sum is 1583293 which is
> prime[119983].
> For prime[680] which is 5087, the sum is 1603597 which is
> prime[121402].
> For prime[696] which is 5233, the sum is 1686239 which is
> prime[127179].
> For prime[708] which is 5351, the sum is 1749833 which is
> prime[131596].
> For prime[734] which is 5563, the sum is 1891889 which is
> prime[141473].
> For prime[762] which is 5807, the sum is 2051167 which is
> prime[152464].
> For prime[768] which is 5849, the sum is 2086159 which is
> prime[154859].
> For prime[776] which is 5897, the sum is 2133121 which is
> prime[158093].
> For prime[780] which is 5939, the sum is 2156813 which is
> prime[159724].
> For prime[784] which is 6007, the sum is 2180741 which is
> prime[161372].
> For prime[808] which is 6211, the sum is 2327399 which is
> prime[171355].
> For prime[814] which is 6263, the sum is 2364833 which is
> prime[173900].
> For prime[820] which is 6301, the sum is 2402537 which is
> prime[176463].
> For prime[836] which is 6427, the sum is 2504323 which is
> prime[183363].
> For prime[844] which is 6529, the sum is 2556187 which is
> prime[186889].
> For prime[848] which is 6563, the sum is 2582401 which is
> prime[188690].
> For prime[852] which is 6581, the sum is 2608699 which is
> prime[190446].
> For prime[926] which is 7243, the sum is 3120833 which is
> prime[224901].
> For prime[942] which is 7433, the sum is 3238237 which is
> prime[232811].
> For prime[984] which is 7757, the sum is 3557303 which is
> prime[253898].
> For prime[992] which is 7853, the sum is 3619807 which is
> prime[258076].
> For prime[1024] which is 8161, the sum is 3875933 which is
> prime[275006].
> For prime[1026] which is 8171, the sum is 3892271 which is
> prime[276090].
> For prime[1030] which is 8219, the sum is 3925069 which is
> prime[278258].
> For prime[1036] which is 8263, the sum is 3974497 which is
> prime[281504].
> For prime[1070] which is 8597, the sum is 4260917 which is
> prime[300308].
> For prime[1098] which is 8819, the sum is 4504663 which is
> prime[316261].
> For prime[1118] which is 9001, the sum is 4682791 which is
> prime[327839].
> For prime[1136] which is 9161, the sum is 4846279 which is
> prime[338451].
> For prime[1142] which is 9209, the sum is 4901431 which is
> prime[342101].
> For prime[1148] which is 9277, the sum is 4956893 which is
> prime[345691].
> For prime[1150] which is 9283, the sum is 4975457 which is
> prime[346897].
> For prime[1178] which is 9511, the sum is 5238847 which is
> prime[363935].
> For prime[1190] which is 9631, the sum is 5353841 which is
> prime[371372].
> For prime[1192] which is 9649, the sum is 5373133 which is
> prime[372606].
> For prime[1196] which is 9689, the sum is 5411839 which is
> prime[375120].
> For prime[1222] which is 9907, the sum is 5666783 which is
> prime[391452].
> For prime[1240] which is 10099, the sum is 5847047 which is
> prime[403009].
> For prime[1256] which is 10247, the sum is 6009791 which is
> prime[413494].
> For prime[1296] which is 10627, the sum is 6426919 which is
> prime[440130].
> For prime[1314] which is 10789, the sum is 6619643 which is
> prime[452439].
> For prime[1322] which is 10867, the sum is 6706397 which is
> prime[457914].
> For prime[1338] which is 11047, the sum is 6881663 which is
> prime[469115].
> For prime[1356] which is 11197, the sum is 7081849 which is
> prime[481857].
> For prime[1386] which is 11491, the sum is 7422539 which is
> prime[503392].
> For prime[1394] which is 11587, the sum is 7514851 which is
> prime[509187].
> For prime[1400] which is 11657, the sum is 7584569 which is
> prime[513573].
> For prime[1408] which is 11731, the sum is 7678183 which is
> prime[519514].
> For prime[1418] which is 11827, the sum is 7796123 which is
> prime[526907].
> For prime[1420] which is 11833, the sum is 7819787 which is
> prime[528412].
> For prime[1446] which is 12073, the sum is 8130767 which is
> prime[547965].
> For prime[1460] which is 12211, the sum is 8300797 which is
> prime[558652].
> For prime[1466] which is 12263, the sum is 8374271 which is
> prime[563255].
> For prime[1474] which is 12343, the sum is 8472683 which is
> prime[569380].
> For prime[1476] which is 12373, the sum is 8497403 which is
> prime[570967].
> For prime[1478] which is 12379, the sum is 8522159 which is
> prime[572524].
> For prime[1494] which is 12511, the sum is 8721413 which is
> prime[585077].
> For prime[1500] which is 12553, the sum is 8796637 which is
> prime[589800].
> For prime[1502] which is 12577, the sum is 8821783 which is
> prime[591345].
> For prime[1510] which is 12641, the sum is 8922677 which is
> prime[597642].
> For prime[1524] which is 12781, the sum is 9100613 which is
> prime[608710].
> For prime[1526] which is 12799, the sum is 9126203 which is
> prime[610285].
> For prime[1546] which is 12979, the sum is 9384209 which is
> prime[626420].
> For prime[1606] which is 13577, the sum is 10180459 which is
> prime[675795].
> For prime[1630] which is 13781, the sum is 10508989 which is
> prime[696179].
> For prime[1632] which is 13799, the sum is 10536577 which is
> prime[697857].
> For prime[1638] which is 13873, the sum is 10619617 which is
> prime[702978].
> For prime[1664] which is 14143, the sum is 10983353 which is
> prime[725501].
> For prime[1690] which is 14419, the sum is 11354851 which is
> prime[748373].
> For prime[1726] which is 14741, the sum is 11879939 which is
> prime[780681].
> For prime[1746] which is 14897, the sum is 12176371 which is
> prime[798853].
> For prime[1752] which is 14957, the sum is 12266017 which is
> prime[804333].
> For prime[1762] which is 15083, the sum is 12416377 which is
> prime[813624].
> For prime[1766] which is 15121, the sum is 12476797 which is
> prime[817306].
> For prime[1770] which is 15149, the sum is 12537353 which is
> prime[820978].
> For prime[1774] which is 15193, the sum is 12598067 which is
> prime[824683].
> For prime[1784] which is 15277, the sum is 12750523 which is
> prime[834058].
> For prime[1842] which is 15791, the sum is 13651669 which is
> prime[888866].
> For prime[1844] which is 15803, the sum is 13683269 which is
> prime[890827].
> For prime[1888] which is 16249, the sum is 14388733 which is
> prime[933747].
> For prime[1912] which is 16493, the sum is 14782039 which is
> prime[957585].
> For prime[1916] which is 16553, the sum is 14848187 which is
> prime[961590].
> For prime[1922] which is 16619, the sum is 14947717 which is
> prime[967573].
> For prime[1944] which is 16843, the sum is 15315721 which is
> prime[989804].
> For prime[1948] which is 16889, the sum is 15383243 which is
> prime[993852].
> For prime[1950] which is 16903, the sum is 15417047 which is
> prime[995857].
>
> So the answer to the original question is not only YES but frequently
> so.
>
> --
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