🤓 A tool to find Julson Primes (additive primes)

My coworker and I were discussing prime numbers, and he was thinking about prime numbers where the sum of their digits is also a prime number. It turns out these are called additive primes, but that's boring. So I'm calling them Julson primes. I wrote a script to see how many there were, compared to regular primes.

The number it will search up to as an argument.

The script lists out all primes, but it will include " Julson" next to the prime if it is a Julson Prime.

The file 'first_million.txt', included in this repository, contains the output for ruby find_julson_primes.rb 1000000

Here is a list of the first thousand Julson Primes:

2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 137, 139, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 241, 263, 269, 281, 283, 311, 313, 317, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 461, 463, 467, 487, 557, 571, 577, 593, 599, 601, 607, 641, 643, 647, 661, 683, 719, 733, 739, 751, 757, 773, 797, 809, 821, 823, 827, 829, 863, 881, 883, 887, 911, 919, 937, 953, 971, 977, 991, 1013, 1019, 1031, 1033, 1039, 1051, 1091, 1093, 1097, 1103, 1109, 1123, 1129, 1163, 1181, 1187, 1213, 1217, 1231, 1237, 1259, 1277, 1279, 1291, 1297, 1301, 1303, 1307, 1321, 1327, 1361, 1367, 1381, 1433, 1439, 1451, 1453, 1459, 1471, 1493, 1499, 1523, 1543, 1549, 1567, 1583, 1613, 1619, 1637, 1657, 1693, 1697, 1709, 1721, 1723, 1741, 1747, 1783, 1787, 1811, 1831, 1871, 1873, 1877, 1901, 1907, 1949, 2003, 2027, 2029, 2063, 2069, 2081, 2083, 2087, 2089, 2111, 2113, 2131, 2137, 2153, 2179, 2203, 2207, 2221, 2243, 2267, 2269, 2281, 2287, 2311, 2333, 2339, 2351, 2357, 2371, 2377, 2393, 2399, 2423, 2441, 2447, 2467, 2531, 2539, 2551, 2557, 2579, 2591, 2593, 2609, 2621, 2647, 2663, 2683, 2687, 2711, 2713, 2719, 2731, 2753, 2777, 2791, 2801, 2803, 2843, 2861, 2917, 2939, 2953, 2957, 2971, 2999, 3011, 3019, 3037, 3079, 3109, 3121, 3163, 3167, 3169, 3181, 3187, 3217, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3323, 3329, 3343, 3347, 3361, 3389, 3413, 3433, 3457, 3491, 3527, 3529, 3541, 3547, 3581, 3583, 3613, 3617, 3631, 3637, 3659, 3671, 3673, 3677, 3691, 3701, 3709, 3727, 3761, 3767, 3833, 3851, 3853, 3907, 3923, 3929, 3943, 3947, 3989, 4001, 4003, 4007, 4021, 4027, 4049, 4111, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4229, 4241, 4243, 4261, 4283, 4289, 4337, 4339, 4357, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4463, 4481, 4483, 4513, 4517, 4519, 4591, 4603, 4621, 4643, 4649, 4663, 4733, 4751, 4793, 4799, 4801, 4861, 4889, 4919, 4931, 4933, 4937, 4951, 4973, 4999, 5011, 5039, 5051, 5059, 5077, 5099, 5101, 5107, 5147, 5167, 5189, 5231, 5233, 5237, 5273, 5279, 5297, 5303, 5309, 5323, 5347, 5381, 5387, 5413, 5417, 5419, 5431, 5437, 5471, 5477, 5501, 5503, 5507, 5521, 5527, 5563, 5581, 5639, 5651, 5653, 5657, 5693, 5701, 5741, 5743, 5783, 5813, 5851, 5879, 5897, 5903, 5923, 5927, 5981, 5987, 6007, 6029, 6043, 6047, 6067, 6089, 6113, 6131, 6133, 6151, 6173, 6197, 6203, 6221, 6229, 6247, 6263, 6269, 6287, 6311, 6317, 6337, 6353, 6359, 6373, 6421, 6427, 6449, 6481, 6551, 6553, 6571, 6599, 6607, 6661, 6689, 6719, 6733, 6737, 6779, 6791, 6803, 6823, 6827, 6841, 6863, 6869, 6911, 6917, 6959, 6971, 6977, 6997, 7013, 7019, 7039, 7057, 7079, 7103, 7109, 7121, 7127, 7129, 7187, 7211, 7213, 7219, 7237, 7253, 7307, 7309, 7321, 7349, 7411, 7417, 7433, 7451, 7457, 7499, 7507, 7523, 7529, 7541, 7547, 7561, 7583, 7589, 7673, 7691, 7699, 7703, 7723, 7727, 7741, 7789, 7817, 7853, 7877, 7879, 7901, 7907, 7949, 8009, 8069, 8081, 8087, 8111, 8117, 8171, 8191, 8209, 8221, 8243, 8263, 8311, 8317, 8353, 8423, 8429, 8443, 8447, 8461, 8513, 8537, 8573, 8597, 8599, 8609, 8623, 8627, 8641, 8663, 8669, 8681, 8689, 8713, 8731, 8753, 8779, 8803, 8807, 8821, 8849, 8861, 8867, 8887, 8933, 8951, 9011, 9013, 9059, 9091, 9103, 9109, 9127, 9161, 9181, 9239, 9257, 9293, 9323, 9341, 9343, 9413, 9419, 9431, 9433, 9437, 9473, 9479, 9491, 9497, 9521, 9587, 9613, 9631, 9677, 9679, 9697, 9721, 9743, 9749, 9767, 9769, 9787, 9811, 9833, 9839, 9851, 9857, 9859, 9901, 9923, 9929, 9941, 9949, 9967, 10037, 10039, 10079, 10091, 10093, 10099, 10103, 10141, 10163, 10169, 10181, 10211, 10253, 10259, 10271, 10273, 10301, 10303, 10321, 10343, 10369, 10433, 10453, 10457, 10459, 10477, 10499, 10501, 10529, 10567, 10589, 10613, 10631, 10639, 10651, 10657, 10691, 10709, 10723, 10729, 10781, 10831, 10837, 10853, 10859, 10891, 10903, 10909, 10949, 11003, 11027, 11047, 11069, 11083, 11087, 11113, 11117, 11119, 11131, 11159, 11171, 11173, 11177, 11197, 11243, 11261, 11287, 11311, 11317, 11351, 11353, 11393, 11399, 11423, 11443, 11447, 11467, 11483, 11489, 11519, 11551, 11579, 11593, 11597, 11621, 11681, 11717, 11719, 11731, 11777, 11801, 11807, 11821, 11827, 11863, 11867, 11933, 11939, 11953, 11971, 12011, 12037, 12071, 12073, 12097, 12101, 12107, 12109, 12143, 12149, 12161, 12163, 12211, 12239, 12251, 12253, 12277, 12301, 12323, 12329, 12343, 12347, 12413, 12433, 12437, 12451, 12457, 12473, 12479, 12491, 12497, 12503, 12527, 12541, 12547, 12569, 12583, 12611, 12613, 12619, 12637, 12653, 12659, 12671, 12703, 12721, 12743, 12763, 12781, 12853, 12893, 12899, 12907, 12923, 12941, 12983, 13001, 13003, 13007, 13009, 13043, 13049, 13063, 13151, 13159, 13171, 13177, 13229, 13241, 13249, 13267, 13313, 13331, 13337, 13339, 13397, 13421, 13441, 13463, 13469, 13487, 13513, 13537, 13553, 13577, 13591, 13627, 13649, 13681, 13711, 13751, 13757, 13799, 13807, 13829, 13841, 13883, 13913, 13931, 13933, 13997, 13999, 14011, 14033, 14051, 14057, 14071, 14107, 14143, 14149, 14251, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14411, 14419, 14431, 14437, 14503, 14543, 14549, 14561, 14563, 14633, 14639, 14653, 14657, 14699, 14723, 14741, 14747, 14783, 14813, 14831, 14851, 14879, 14891, 14897, 14923, 14969, 15061, 15083, 15131, 15137, 15139, 15173, 15193, 15227, 15241, 15263, 15269, 15287, 15313, 15319, 15331, 15359, 15373, 15377, 15391, 15401, 15427, 15443, 15461, 15467, 15511, 15551, 15601, 15607, 15629, 15641, 15643, 15647, 15661, 15683, 15731, 15733, 15737, 15773, 15791, 15797, 15803, 15809, 15823, 15881, 15887, 15889, 15913, 15959, 15971, 16033, 16057, 16073, 16091, 16097, 16103, 16127, 16141, 16183, 16187, 16217, 16231, 16253, 16273, 16301, 16349, 16361, 16363, 16381, 16411, 16417, 16433, 16451, 16453, 16493, 16529, 16547, 16561, 16619, 16631, 16633, 16651, 16673, 16691, 16699, 16703, 16741, 16763, 16787, 16811, 16831, 16871, 16879, 16901, 16903, 16921, 16943, 16987, 17021, 17027, 17029, 17041, 17047, 17117, 17137, 17159, 17191, 17203, 17207, 17209, 17317, 17333, 17351, 17393, 17401, 17443, 17483, 17489, 17519, 17551, 17573, 17579, 17597, 17599, 17609, 17623, 17627, 17669, 17681, 17713, 17807, 17911, 17939, 17957, 17959, 17977, 18013, 18059, 18077, 18121, 18127, 18143, 18149, 18181, 18211, 18217, 18233, 18251, 18253, 18257, 18301, 18307, 18329, 18341, 18413, 18433, 18451, 18503, 18521, 18523, 18541, 18587, 18617, 18671, 18679