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Block #1,424,934

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/23/2016, 8:53:19 AM Β· Difficulty 10.7698 Β· 5,419,839 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3656aba02b1a53bfebf8adcd698dd4bf5530d89878e80c5995f2b8974ccf97c7
View on Chainz β†—

Height

#1,424,934

Difficulty

10.769844

Transactions

2

Size

3.46 KB

Version

2

Bits

0ac51480

Nonce

955,912,542

Timestamp

1/23/2016, 8:53:19 AM

Confirmations

5,419,839

Mined by

⛏️ P2SHAZq4RNnoYz16bjaiZGXoKZH9c5zJ295WxY

Merkle Root

4478e71826b27a3156cd9c9bad989d7a702796c479056abd6d3951eac607296e
Transactions (2)
Coinbase408b29fcfaae77…ff7693d6114470
1 in β†’ 1 out8.6600 XPM109 B
AZq4RNno…zJ295WxY
dba52e88714a39…35c8efa548c797
22 in β†’ 2 out268.6623 XPM3.26 KB
AVyiUW3Z…PLtb1yHrATB74oXY…stL4TZyf
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.

4.454 Γ— 10⁹³(94-digit number)
44544418377967063481…99405213682765712641
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
4.454 Γ— 10⁹³(94-digit number)
44544418377967063481…99405213682765712641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.908 Γ— 10⁹³(94-digit number)
89088836755934126963…98810427365531425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.781 Γ— 10⁹⁴(95-digit number)
17817767351186825392…97620854731062850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.563 Γ— 10⁹⁴(95-digit number)
35635534702373650785…95241709462125701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.127 Γ— 10⁹⁴(95-digit number)
71271069404747301570…90483418924251402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.425 Γ— 10⁹⁡(96-digit number)
14254213880949460314…80966837848502804481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.850 Γ— 10⁹⁡(96-digit number)
28508427761898920628…61933675697005608961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.701 Γ— 10⁹⁡(96-digit number)
57016855523797841256…23867351394011217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.140 Γ— 10⁹⁢(97-digit number)
11403371104759568251…47734702788022435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.280 Γ— 10⁹⁢(97-digit number)
22806742209519136502…95469405576044871681
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:58,002,597 XPMΒ·at block #6,844,772 Β· updates every 60s
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