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Block #267,591

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/21/2013, 10:01:27 AM Β· Difficulty 9.9588 Β· 6,537,674 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e1f0ef2ae986fcdfefbf8920b0661ec4663a0244827ea2de3e6c87dc1829dab8
View on Chainz β†—

Height

#267,591

Difficulty

9.958787

Transactions

1

Size

205 B

Version

2

Bits

09f5730a

Nonce

21,794

Timestamp

11/21/2013, 10:01:27 AM

Confirmations

6,537,674

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

ec8d78cee74942f371ff29e8871282624c6988792bd75a6decb931229e27008e
Transactions (1)
Coinbaseec8d78cee74942…b931229e27008e
1 in β†’ 1 out10.0700 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.

1.580 Γ— 10⁹³(94-digit number)
15808340472090297230…18454006439875571201
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
1.580 Γ— 10⁹³(94-digit number)
15808340472090297230…18454006439875571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.161 Γ— 10⁹³(94-digit number)
31616680944180594460…36908012879751142401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.323 Γ— 10⁹³(94-digit number)
63233361888361188921…73816025759502284801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.264 Γ— 10⁹⁴(95-digit number)
12646672377672237784…47632051519004569601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.529 Γ— 10⁹⁴(95-digit number)
25293344755344475568…95264103038009139201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.058 Γ— 10⁹⁴(95-digit number)
50586689510688951137…90528206076018278401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.011 Γ— 10⁹⁡(96-digit number)
10117337902137790227…81056412152036556801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.023 Γ— 10⁹⁡(96-digit number)
20234675804275580454…62112824304073113601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.046 Γ— 10⁹⁡(96-digit number)
40469351608551160909…24225648608146227201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.093 Γ— 10⁹⁡(96-digit number)
80938703217102321819…48451297216292454401
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:57,686,191 XPMΒ·at block #6,805,264 Β· updates every 60s
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