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Scala, 59 Bytes

def f(t:BigInt)=t.isProbablePrime(t.bitLength*4bitLength*9)&(1+t)%2==0

This function requires the input to be a BigInt. You can easily convert a string "162259276829213363391578010288127" (2**107-1 is a Mersenne prime) into BigInt by doing BigInt("162259276829213363391578010288127"). It might go wrong as the name of isProbablePrime() method suggests. But the probability is not more than 0.5^(t.bigLength)*4*9.

Standalone script version is 72 bytes long.

val t=BigInt(args(0));print(t.isProbablePrime(t.bitLength*4bitLength*9)&(1+t)%2==0)

Assume we save it as "t.scala", then then program can be run as

>scala t.scala 162259276829213363391578010288127
>true

Scala, 59 Bytes

def f(t:BigInt)=t.isProbablePrime(t.bitLength*4)&(1+t)%2==0

This function requires the input to be a BigInt. You can easily convert a string "162259276829213363391578010288127" (2**107-1 is a Mersenne prime) into BigInt by doing BigInt("162259276829213363391578010288127"). It might go wrong as the name of isProbablePrime() method suggests. But the probability is not more than 0.5^(t.bigLength)*4.

Standalone script version is 72 bytes long.

val t=BigInt(args(0));print(t.isProbablePrime(t.bitLength*4)&(1+t)%2==0)

Assume we save it as "t.scala", then then program can be run as

>scala t.scala 162259276829213363391578010288127
>true

Scala, 59 Bytes

def f(t:BigInt)=t.isProbablePrime(t.bitLength*9)&(1+t)%2==0

This function requires the input to be a BigInt. You can easily convert a string "162259276829213363391578010288127" (2**107-1 is a Mersenne prime) into BigInt by doing BigInt("162259276829213363391578010288127"). It might go wrong as the name of isProbablePrime() method suggests. But the probability is not more than 0.5^(t.bigLength)*9.

Standalone script version is 72 bytes long.

val t=BigInt(args(0));print(t.isProbablePrime(t.bitLength*9)&(1+t)%2==0)

Assume we save it as "t.scala", then then program can be run as

>scala t.scala 162259276829213363391578010288127
>true
1
source | link

Scala, 59 Bytes

def f(t:BigInt)=t.isProbablePrime(t.bitLength*4)&(1+t)%2==0

This function requires the input to be a BigInt. You can easily convert a string "162259276829213363391578010288127" (2**107-1 is a Mersenne prime) into BigInt by doing BigInt("162259276829213363391578010288127"). It might go wrong as the name of isProbablePrime() method suggests. But the probability is not more than 0.5^(t.bigLength)*4.

Standalone script version is 72 bytes long.

val t=BigInt(args(0));print(t.isProbablePrime(t.bitLength*4)&(1+t)%2==0)

Assume we save it as "t.scala", then then program can be run as

>scala t.scala 162259276829213363391578010288127
>true