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balanced primes
A prime is said to be balanced if it is the average of the two surrounding primes, i.e., it is at equal distance from previous prime and next prime.

For example, 53 is a balanced prime since it is the average of the two primes 47 and 59.

The smallest 3 × 3 magic square made of balanced primes is

66024233189353916675727
28463867183905638317259
20105399488758730178703

The first balanced primes are 5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, 1187, 1223, 1367, 1511 more terms

Balanced primes can also be... (you may click on names or numbers and on + to get more values)

aban 53 157 173 211 257 + 9999000689 alternating 563 947 2903 2963 6323 + 989892367 amenable 53 157 173 257 373 + 999998789 apocalyptic 157 977 1103 1753 2287 + 29873 arithmetic 53 157 173 211 257 + 9999937 bemirp 18616681 168910801 199109681 1088900611 1161111661 + 1969081091 c.decagonal 211 20161 135301 183361 286801 + 9897022951 c.heptagonal 176401 890821 1545461 1578193 8262913 + 9583951693 c.pentagonal 11731 17431 17851 839551 8868931 + 9482550391 c.square 15313 20201 156241 353641 1035361 + 9992597081 c.triangular 412651 1282051 4670191 7395931 7876459 + 9787991431 Chen 53 157 211 257 263 + 99999617 congruent 53 157 173 257 263 + 9997327 constructible 257 Cunningham 257 13457 30977 33857 98597 + 9748402757 Curzon 53 173 593 653 4409 + 199999661 cyclic 53 157 173 211 257 + 9999937 d-powerful 373 17483 22447 23327 26393 + 9923477 de Polignac 373 977 3637 4013 4691 + 99999617 deficient 53 157 173 211 257 + 9999937 dig.balanced 563 653 2417 7823 7841 + 199987841 economical 53 157 173 211 257 + 19999981 emirp 157 733 1103 1223 1511 + 199999661 equidigital 53 157 173 211 257 + 19999981 esthetic 34543 432343 3212323 5434343 343232101 + 6789898987 evil 53 257 263 373 593 + 999998789 fibodiv 123047543 Friedman 19739 74897 128153 156241 161053 + 885727 good prime 53 257 563 593 733 + 199880953 happy 263 563 653 1511 2417 + 9996823 hex 22447 35317 45757 73477 151201 + 9974545747 Hogben 157 211 1123 3307 5113 + 9945973171 Honaker 263 7523 11731 13457 15193 + 999821261 iban 173 211 373 1103 1123 + 777103 inconsummate 173 563 3307 3733 4409 + 993869 junction 6317 6323 7823 8117 10607 + 99986251 katadrome 53 653 9871 96431 Leyland 593 32993 lonely 53 211 lucky 211 1123 3307 3313 4993 + 9983977 m-pointer 1123 21911 3116111 11413111 12111331 + 1111131821 magnanimous 607 42209 metadrome 157 257 1367 13457 12356789 modest 211 733 23333 29333 40111 + 1999002079 nialpdrome 53 211 653 733 977 + 9999997543 oban 53 373 563 593 607 + 977 odious 157 173 211 563 607 + 999996329 Ormiston 34631 66431 76579 122579 145879 + 1999965379 palindromic 373 11411 30103 34543 35753 + 996989699 palprime 373 11411 30103 34543 35753 + 996989699 pancake 211 947 4657 9871 40471 + 9999313237 panconsummate 53 211 257 pernicious 157 173 211 257 563 + 9997219 Pierpont 257 18433 plaindrome 157 257 1123 1223 1367 + 6888899999 prime 53 157 173 211 257 + 9999997543 primeval 1367 Proth 257 4993 9473 18433 30977 + 9963962369 repunit 157 211 1123 3307 5113 + 9945973171 self 53 211 1223 3313 5113 + 999979397 self-describing 17331031 21322319 32272733 1341441841 1722311033 + 4442274227 star 3313 12973 15913 986581 1527121 + 9942603337 strobogrammatic 688889 1068901 1681891 11896811 166906991 + 1906699061 super-d 1123 4013 4597 5113 7823 + 9997219 truncatable prime 53 173 373 593 653 + 9391564373 uban 53 1000099 6000047 7000003 7000033 + 9099000013 Ulam 53 607 1103 4409 7583 + 9992681 undulating 373 upside-down 7823 92581 3355577 14991169 16746349 + 9882648221 weakly prime 3326489 21089489 21668839 27245539 38178211 + 9994090871 zygodrome 3355577 5555777 7722277 7799333 8884433 + 9993355511