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Block #265,247

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/19/2013, 9:40:21 AM Β· Difficulty 9.9630 Β· 6,544,450 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
1330b5a3ee8011e35f4b49c76213541a59fc86b3ce734ace1c67ff0b7e52d929
View on Chainz β†—

Height

#265,247

Difficulty

9.962995

Transactions

2

Size

1.02 KB

Version

2

Bits

09f686d8

Nonce

5,864

Timestamp

11/19/2013, 9:40:21 AM

Confirmations

6,544,450

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

ca8a8f24ae879b7875aebc32f16d0f00ab1f74cedb3b5344f2a10965c4348454
Transactions (2)
Coinbase3deca1e11ea02b…1290e83f13efdd
1 in β†’ 2 out10.0700 XPM136 B
AKcbk49N…GJbKa7j1AHsw4d6U…EnM8UXNZ
4b0ce11fead59f…16b51b654aef40
5 in β†’ 2 out280.0322 XPM817 B
Abj8VRjK…oT2ZmeqvAXcyHdj3…oKn7rQwz
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.470 Γ— 10⁹⁡(96-digit number)
44705807847397031311…05406951285008000641
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
4.470 Γ— 10⁹⁡(96-digit number)
44705807847397031311…05406951285008000641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.941 Γ— 10⁹⁡(96-digit number)
89411615694794062623…10813902570016001281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.788 Γ— 10⁹⁢(97-digit number)
17882323138958812524…21627805140032002561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.576 Γ— 10⁹⁢(97-digit number)
35764646277917625049…43255610280064005121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.152 Γ— 10⁹⁢(97-digit number)
71529292555835250098…86511220560128010241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.430 Γ— 10⁹⁷(98-digit number)
14305858511167050019…73022441120256020481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.861 Γ— 10⁹⁷(98-digit number)
28611717022334100039…46044882240512040961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.722 Γ— 10⁹⁷(98-digit number)
57223434044668200078…92089764481024081921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.144 Γ— 10⁹⁸(99-digit number)
11444686808933640015…84179528962048163841
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,721,653 XPMΒ·at block #6,809,696 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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