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Congratulations on your new job, I wish you success, as indicated in the previous replies, if possible it is best to give a two week notice. Address your letter of resignation to your supervisor and cc: a copy to Human Resources, don't forget to indicate the last day you will be working in the body of your letter.
Best wishes to you!
NewDay12
Since you've stated you'll start the new job in 2 weeks, I'd give a 2 week notice. However, since you've been at your current job for just a few weeks, I would not consider it a responsibility to my current employer. To keep a current pay check flowing, I'd go with leaving one job and going to the next. However, if there are matters you need to tend to before undertaking the new position, I'd give the current employer a modest notice and take my leave. Just sharing some options.. Since the current jobs market is geared toward the employer, the opportunity presented you to make a choice is empowering. Were I you, I'd go with what my "gut" told me.
Best wishes, and good luck!