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Block #672,062

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/10/2014, 4:37:35 PM Β· Difficulty 10.9645 Β· 6,168,699 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e1861c3aed4471c0ce646bff8bc663478eb752b9644a7f8330a7bd7c45a9467d
View on Chainz β†—

Height

#672,062

Difficulty

10.964525

Transactions

1

Size

206 B

Version

2

Bits

0af6eb23

Nonce

1,861,129,791

Timestamp

8/10/2014, 4:37:35 PM

Confirmations

6,168,699

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8006e6505ec5253663e3b6c5588a6550d7d5fe38c00ced9ebf44dd10eacc81b9
Transactions (1)
Coinbase8006e6505ec525…44dd10eacc81b9
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
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.

7.352 Γ— 10⁹⁡(96-digit number)
73525135366395946055…83361573551069041281
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
7.352 Γ— 10⁹⁡(96-digit number)
73525135366395946055…83361573551069041281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.470 Γ— 10⁹⁢(97-digit number)
14705027073279189211…66723147102138082561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.941 Γ— 10⁹⁢(97-digit number)
29410054146558378422…33446294204276165121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.882 Γ— 10⁹⁢(97-digit number)
58820108293116756844…66892588408552330241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.176 Γ— 10⁹⁷(98-digit number)
11764021658623351368…33785176817104660481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.352 Γ— 10⁹⁷(98-digit number)
23528043317246702737…67570353634209320961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.705 Γ— 10⁹⁷(98-digit number)
47056086634493405475…35140707268418641921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.411 Γ— 10⁹⁷(98-digit number)
94112173268986810951…70281414536837283841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.882 Γ— 10⁹⁸(99-digit number)
18822434653797362190…40562829073674567681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.764 Γ— 10⁹⁸(99-digit number)
37644869307594724380…81125658147349135361
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:57,970,430 XPMΒ·at block #6,840,760 Β· updates every 60s
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