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A large XP lamp can be bought from Gypsy Aris' Reward Shop for five silver pennies, which are rewarded after completing or replaying Dimension of Disaster. This is the type of lamp available if you've only completed up to the hard set of the New Varrock Tasks. The lamp can only be bought once per week, resetting at 00:00 UTC on Wednesday. It gives the same amount of experience as a regular large XP lamp:

Skill levelExperienceSkill levelExperienceSkill levelExperience
1250342,237679,076
2276352,332689,516
3308362,434699,880
4340372,5407010,371
5373382,6487110,772
6416392,7667211,237
7492402,8827311,786
8508413,0087412,328
9777423,1387512,855
10614433,2727613,358
11680443,4147713,980
12752453,5587814,587
13822463,7167915,169
14916473,8828015,920
151,008484,0508116,664
161,046494,2208217,390
171,096504,4048318,087
181,140514,5938419,048
191,192524,8008519,674
201,240534,9988620,132
211,298545,2188721,502
221,348555,4488822,370
231,408565,6888923,690
241,470575,9409024,486
251,536586,1849125,806
261,596596,4669226,458
271,621606,7379327,714
281,656617,0309428,944
291,812627,3429530,130
301,892637,6459632,258
311,973648,0189733,390
322,056658,43298+34,408
332,144668,686
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