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Block #439,418

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/11/2014, 4:24:32 PM Β· Difficulty 10.3595 Β· 6,375,634 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
887d5b91c29d3dabd8261e24ce206d9a1bc89042f63555b9dbb94132a16db008
View on Chainz β†—

Height

#439,418

Difficulty

10.359537

Transactions

1

Size

199 B

Version

2

Bits

0a5c0a99

Nonce

77,779

Timestamp

3/11/2014, 4:24:32 PM

Confirmations

6,375,634

Mined by

⛏️ P2SHARYuCmXbMZuxj6vde8hvy7nx16HnxRmwtf

Merkle Root

0523757b792d8fb29441cc0f84040227f97bd8cd0774fb4306250a94d0cf5516
Transactions (1)
Coinbase0523757b792d8f…250a94d0cf5516
1 in β†’ 1 out9.3000 XPM109 B
ARYuCmXb…HnxRmwtf
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.

2.239 Γ— 10⁹⁡(96-digit number)
22392211486055972332…90086444779564528641
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
2.239 Γ— 10⁹⁡(96-digit number)
22392211486055972332…90086444779564528641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.478 Γ— 10⁹⁡(96-digit number)
44784422972111944665…80172889559129057281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.956 Γ— 10⁹⁡(96-digit number)
89568845944223889331…60345779118258114561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.791 Γ— 10⁹⁢(97-digit number)
17913769188844777866…20691558236516229121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.582 Γ— 10⁹⁢(97-digit number)
35827538377689555732…41383116473032458241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.165 Γ— 10⁹⁢(97-digit number)
71655076755379111465…82766232946064916481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.433 Γ— 10⁹⁷(98-digit number)
14331015351075822293…65532465892129832961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.866 Γ— 10⁹⁷(98-digit number)
28662030702151644586…31064931784259665921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.732 Γ— 10⁹⁷(98-digit number)
57324061404303289172…62129863568519331841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.146 Γ— 10⁹⁸(99-digit number)
11464812280860657834…24259727137038663681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,764,507 XPMΒ·at block #6,815,051 Β· updates every 60s
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