A skill-specific medium XP lamp can be obtained from Zombie Monkeys community scenario. When rubbed, it grants the player a definite amount of experience scaled to the selected skill level. The experience gained is the same from level 98 to 120.
Previously it was a fairly common prize reward from Treasure Hunter, where it could be gained for any skill that had not been frozen. In addition to coming in a skill-specific form, where the skill was specified by the lamp, players could also receive lamps where they could choose the skill they'd gain experience in. These were replaced on the Squeal of Fortune with medium prismatic lamps.
An update on 12 October 2012 replaced skill-specific medium lamps in Construction, Crafting, Farming, Herblore, Smithing and Summoning by crates containing training items for the skills. However, it is still possible to receive a medium XP lamp for these skills instead.
On 7 April 2014 medium XP lamps for F2P skills became claimable by F2P players. Free players could now also convert them to 5,000 coins.

The reward interface of a Medium XP lamp.

The confirmation message displayed when rubbing a skill-specific XP lamp.
If you use a medium XP lamp on Dungeoneering, dungeoneering tokens will not be awarded.
Experience table[]
The following is an experience table detailing the number of experience received from a medium lamp for any given skill level:
Skill level | Experience | Skill level | Experience | Skill level | Experience | ||
---|---|---|---|---|---|---|---|
1 | 125 | 34 | 1,118 | 67 | 4,538 | ||
2 | 138 | 35 | 1,166 | 68 | 4,758 | ||
3 | 154 | 36 | 1,217 | 69 | 4,940 | ||
4 | 170 | 37 | 1,270 | 70 | 5,185 | ||
5 | 186 | 38 | 1,324 | 71 | 5,386 | ||
6 | 208 | 39 | 1,383 | 72 | 5,618 | ||
7 | 246 | 40 | 1,441 | 73 | 5,893 | ||
8 | 254 | 41 | 1,504 | 74 | 6,164 | ||
9 | 388 | 42 | 1,569 | 75 | 6,427 | ||
10 | 307 | 43 | 1,636 | 76 | 6,679 | ||
11 | 340 | 44 | 1,707 | 77 | 6,990 | ||
12 | 376 | 45 | 1,779 | 78 | 7,293 | ||
13 | 411 | 46 | 1,858 | 79 | 7,584 | ||
14 | 458 | 47 | 1,941 | 80 | 7,960 | ||
15 | 504 | 48 | 2,025 | 81 | 8,332 | ||
16 | 523 | 49 | 2,110 | 82 | 8,695 | ||
17 | 548 | 50 | 2,202 | 83 | 9,043 | ||
18 | 570 | 51 | 2,296 | 84 | 9,524 | ||
19 | 596 | 52 | 2,400 | 85 | 9,837 | ||
20 | 620 | 53 | 2,499 | 86 | 10,066 | ||
21 | 649 | 54 | 2,609 | 87 | 10,751 | ||
22 | 674 | 55 | 2,724 | 88 | 11,185 | ||
23 | 704 | 56 | 2,844 | 89 | 11,845 | ||
24 | 735 | 57 | 2,970 | 90 | 12,243 | ||
25 | 768 | 58 | 3,092 | 91 | 12,903 | ||
26 | 798 | 59 | 3,233 | 92 | 13,229 | ||
27 | 810 | 60 | 3,368 | 93 | 13,857 | ||
28 | 828 | 61 | 3,515 | 94 | 14,472 | ||
29 | 906 | 62 | 3,671 | 95 | 15,065 | ||
30 | 946 | 63 | 3,822 | 96 | 16,129 | ||
31 | 986 | 64 | 4,009 | 97 | 16,695 | ||
32 | 1,028 | 65 | 4,216 | 98+ | 17,204 | ||
33 | 1,072 | 66 | 4,343 |