The calculator I always wanted

[vanLudwig]

I wondered for which integers n is the sum of the first n primes itself prime? 2 is prime. 2+3=5 is prime. 2+3+5=10 is not. 2+3+5+7=17 is prime. 2+3+5+7+11=28 is not. Turns out, it happens a lot.

$$\texttt{Select}\left ( \left \{ n \right \}_{n=1}^{2500}, n \mapsto \sum_{i=1}^{n} p_{i}\in \mathbb{P} \right )$$
{1,2,4,6,12,14,60,64,96,100,102,108,114,122,124,130,132,146,152,158,162,178,192,​
198,204,206,208,214,216,296,308,326,328,330,332,334,342,350,356,358,426,446,458,​
460,464,480,484,488,512,530,536,548,568,620,630,676,680,696,708,734,762,768,776,​
780,784,808,814,820,836,844,848,852,926,942,984,992,1024,1026,1030,1036,1070,
1098,1118,1136,1142,1148,1150,1178,1190,1192,1196,1222,1240,1256,1296,1314,1322,​
1338,1356,1386,1394,1400,1408,1418,1420,1446,1460,1466,1474,1476,1478,1494,1500,​
1502,1510,1524,1526,1546,1606,1630,1632,1638,1664,1690,1726,1746,1752,1762,1766,​
1770,1774,1784,1842,1844,1888,1912,1916,1922,1944,1948,1950,1956,2032,2060,2084,​
2094,2106,2128,2130,2132,2184,2186,2200,2210,2222,2262,2268,2288,2310,2324,2342,​
2360,2372,2380,2432,2436,2438,2444,2448,2450,2460,2466,2496}

(This uses catalog functions Select, Table, Function, Sum, Prime, Element, and Primes)