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Block #1,266,556

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2015, 10:02:40 AM Β· Difficulty 10.8196 Β· 5,542,916 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
99c7733049b3fc0919a6d92fe8517ee877b5ba953dc2475d9774d8b5cd3462cb
View on Chainz β†—

Height

#1,266,556

Difficulty

10.819602

Transactions

2

Size

574 B

Version

2

Bits

0ad1d16b

Nonce

354,873,900

Timestamp

10/4/2015, 10:02:40 AM

Confirmations

5,542,916

Mined by

⛏️ P2SHAPe1kz6yiwDxF9atJLTTM3K5U7MN5vEVXu

Merkle Root

618aac8b5255daff1938db0eb1d899fe035ee27bc4b1744631656d09b4660e12
Transactions (2)
Coinbase2b6620c4d7dd70…1e4966478e20c4
1 in β†’ 1 out8.5400 XPM110 B
APe1kz6y…MN5vEVXu
f7debaa089be41…3bbb8883b0bfb6
2 in β†’ 2 out0.4345 XPM374 B
ALCRxwEr…7C1LtwcDAKgSKRsF…JMpq1XPw
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.

1.942 Γ— 10⁹⁴(95-digit number)
19429608747567023959…15978538901040379841
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
1.942 Γ— 10⁹⁴(95-digit number)
19429608747567023959…15978538901040379841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.885 Γ— 10⁹⁴(95-digit number)
38859217495134047918…31957077802080759681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.771 Γ— 10⁹⁴(95-digit number)
77718434990268095836…63914155604161519361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.554 Γ— 10⁹⁡(96-digit number)
15543686998053619167…27828311208323038721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.108 Γ— 10⁹⁡(96-digit number)
31087373996107238334…55656622416646077441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.217 Γ— 10⁹⁡(96-digit number)
62174747992214476669…11313244833292154881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.243 Γ— 10⁹⁢(97-digit number)
12434949598442895333…22626489666584309761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.486 Γ— 10⁹⁢(97-digit number)
24869899196885790667…45252979333168619521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.973 Γ— 10⁹⁢(97-digit number)
49739798393771581335…90505958666337239041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.947 Γ— 10⁹⁢(97-digit number)
99479596787543162670…81011917332674478081
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:57,719,848 XPMΒ·at block #6,809,471 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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