Definition:Balanced Prime/Sequence
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Sequence
The sequence of balanced primes begins:
- $5, 53, 157, 173, 211, 257, 263, 373, 563, 593, 607, 653, 733, 947, 977, 1103, 1123, \ldots$
This sequence is A006562 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Examples
| \(\ds 2 \times 5\) | \(=\) | \(\ds 3 + 7\) | ||||||||||||
| \(\ds 2 \times 53\) | \(=\) | \(\ds 47 + 59\) | ||||||||||||
| \(\ds 2 \times 157\) | \(=\) | \(\ds 151 + 163\) | ||||||||||||
| \(\ds 2 \times 173\) | \(=\) | \(\ds 167 + 179\) | ||||||||||||
| \(\ds 2 \times 211\) | \(=\) | \(\ds 199 + 223\) | ||||||||||||
| \(\ds 2 \times 257\) | \(=\) | \(\ds 251 + 263\) | ||||||||||||
| \(\ds 2 \times 263\) | \(=\) | \(\ds 257 + 269\) | ||||||||||||
| \(\ds 2 \times 373\) | \(=\) | \(\ds 367 + 379\) | ||||||||||||
| \(\ds 2 \times 563\) | \(=\) | \(\ds 557 + 569\) | ||||||||||||
| \(\ds 2 \times 593\) | \(=\) | \(\ds 587 + 599\) | ||||||||||||
| \(\ds 2 \times 607\) | \(=\) | \(\ds 601 + 613\) |
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $257$