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Block #247,266

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/6/2013, 3:58:58 PM Β· Difficulty 9.9648 Β· 6,547,625 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
69c77320bca9c0e82987a8287047ed7232bf7343c700b817350554b6335c56b2
View on Chainz β†—

Height

#247,266

Difficulty

9.964792

Transactions

1

Size

207 B

Version

2

Bits

09f6fc9b

Nonce

112,178

Timestamp

11/6/2013, 3:58:58 PM

Confirmations

6,547,625

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

747f784463ee5e5714f07b24bcfcd14932a867ad29a77b9a646259f727b6c47e
Transactions (1)
Coinbase747f784463ee5e…6259f727b6c47e
1 in β†’ 1 out10.0600 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.427 Γ— 10⁹⁷(98-digit number)
54278889548217558002…34236141331970778881
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
5.427 Γ— 10⁹⁷(98-digit number)
54278889548217558002…34236141331970778881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.085 Γ— 10⁹⁸(99-digit number)
10855777909643511600…68472282663941557761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.171 Γ— 10⁹⁸(99-digit number)
21711555819287023200…36944565327883115521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.342 Γ— 10⁹⁸(99-digit number)
43423111638574046401…73889130655766231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.684 Γ— 10⁹⁸(99-digit number)
86846223277148092803…47778261311532462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.736 Γ— 10⁹⁹(100-digit number)
17369244655429618560…95556522623064924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.473 Γ— 10⁹⁹(100-digit number)
34738489310859237121…91113045246129848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.947 Γ— 10⁹⁹(100-digit number)
69476978621718474243…82226090492259696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.389 Γ— 10¹⁰⁰(101-digit number)
13895395724343694848…64452180984519393281
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:57,603,164 XPMΒ·at block #6,794,890 Β· updates every 60s
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