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Block #2,237,881

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2017, 9:49:25 AM Β· Difficulty 10.9461 Β· 4,601,238 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
79ac26d1a450d3e7d05c00b3a5e91c5f6f84a315e2f33058158ed9e141447d60
View on Chainz β†—

Height

#2,237,881

Difficulty

10.946143

Transactions

1

Size

200 B

Version

2

Bits

0af23668

Nonce

1,407,850,598

Timestamp

8/5/2017, 9:49:25 AM

Confirmations

4,601,238

Mined by

⛏️ P2SHAb8ZGejVwEs1zJNcPwmJwSyV7WVK7pqhqG

Merkle Root

3284dc1c0003b53f9057dc88084ab405e461adb8a4d0c7d50147605a2e5ed2c8
Transactions (1)
Coinbase3284dc1c0003b5…47605a2e5ed2c8
1 in β†’ 1 out8.3300 XPM110 B
Ab8ZGejV…VK7pqhqG
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.

2.981 Γ— 10⁹⁡(96-digit number)
29812106271400690075…26292479927912274721
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
2.981 Γ— 10⁹⁡(96-digit number)
29812106271400690075…26292479927912274721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.962 Γ— 10⁹⁡(96-digit number)
59624212542801380150…52584959855824549441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.192 Γ— 10⁹⁢(97-digit number)
11924842508560276030…05169919711649098881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.384 Γ— 10⁹⁢(97-digit number)
23849685017120552060…10339839423298197761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.769 Γ— 10⁹⁢(97-digit number)
47699370034241104120…20679678846596395521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.539 Γ— 10⁹⁢(97-digit number)
95398740068482208240…41359357693192791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.907 Γ— 10⁹⁷(98-digit number)
19079748013696441648…82718715386385582081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.815 Γ— 10⁹⁷(98-digit number)
38159496027392883296…65437430772771164161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.631 Γ— 10⁹⁷(98-digit number)
76318992054785766592…30874861545542328321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.526 Γ— 10⁹⁸(99-digit number)
15263798410957153318…61749723091084656641
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:57,957,227 XPMΒ·at block #6,839,118 Β· updates every 60s
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