2^1-1=1

(2^1-1)+(3^2-1)=1+8=9

(2^1-1)+(3^2-1)+(4^3-1)=1+8+63=72

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)=1+8+63+624=696

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)=1+8+63+624+7775=8471

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)+(7^6-1)=1+8+63+624+7775+117648=126119

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)+(7^6-1)+(8^7-1)=1+8+63+624+7775+117648+2097151=2223270

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)+(7^6-1)+(8^7-1)+(9^8-1)=1+8+63+624+7775+117648+2097151+43046720=45269990

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)+(7^6-1)+(8^7-1)+(9^8-1)+(10^9-1)=1+8+63+624+7775+117648+2097151+43046720+999999999=1045269989

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)+(7^6-1)+(8^7-1)+(9^8-1)+(10^9-1)+(11^10-1)=1+8+63+624+7775+117648+2097151+43046720+999999999+25937424600=26982694589

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)+(7^6-1)+(8^7-1)+(9^8-1)+(10^9-1)+(11^10-1)+(12^11-1)=1+8+63+624+7775+117648+2097151+43046720+999999999+25937424600+743008370687=769991065276

(2^1-1)+(3^2-1)+(4^3-1)+(5^4-1)+(6^5-1)+(7^6-1)+(8^7-1)+(9^8-1)+(10^9-1)+(11^10-1)+(12^11-1)+(13^12-1)=1+8+63+624+7775+117648+2097151+43046720+999999999+25937424600+743008370687+23298085122480=24068076187756

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Therefore, the next number is 24068076187756. The giveaway was 45269990 and 1045269989, which differ by 10^9-1=999999999.