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A Central Equipment Identity Register (CEIR) is a database of mobile equipment identifiers (IMEI – for networks of GSM standard, MEID – for networks of CDMA standard). Such an identifier is assigned to each SIM slot of the mobile device.
The last number of the IMEI is a check digit, calculated using the Luhn algorithm, as defined in the IMEI Allocation and Approval Guidelines: The Check Digit shall be calculated according to Luhn formula (ISO/IEC 7812). (See GSM 02.16 / 3GPP 22.016). The Check Digit is a function of all other digits in the IMEI.