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Block #2,094,133

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2017, 10:02:21 AM Β· Difficulty 10.8715 Β· 4,746,535 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a4857c9b3593b6cd59ad3af0d76e88d50dfb7d2a1505137789e8bdf59233188b
View on Chainz β†—

Height

#2,094,133

Difficulty

10.871476

Transactions

1

Size

200 B

Version

2

Bits

0adf190b

Nonce

1,274,401,024

Timestamp

4/30/2017, 10:02:21 AM

Confirmations

4,746,535

Mined by

⛏️ P2SHAcEwFpiCbWjYToVzrysbEidXtAESppLCgg

Merkle Root

c95ba6a3ec359ec78e729309c6f318e5787391e56a0515753324d38b131ee074
Transactions (1)
Coinbasec95ba6a3ec359e…24d38b131ee074
1 in β†’ 1 out8.4500 XPM109 B
AcEwFpiC…ESppLCgg
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.

2.230 Γ— 10⁹⁢(97-digit number)
22308276279686629623…61390955161124736001
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
2.230 Γ— 10⁹⁢(97-digit number)
22308276279686629623…61390955161124736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.461 Γ— 10⁹⁢(97-digit number)
44616552559373259247…22781910322249472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.923 Γ— 10⁹⁢(97-digit number)
89233105118746518495…45563820644498944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.784 Γ— 10⁹⁷(98-digit number)
17846621023749303699…91127641288997888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.569 Γ— 10⁹⁷(98-digit number)
35693242047498607398…82255282577995776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.138 Γ— 10⁹⁷(98-digit number)
71386484094997214796…64510565155991552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.427 Γ— 10⁹⁸(99-digit number)
14277296818999442959…29021130311983104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.855 Γ— 10⁹⁸(99-digit number)
28554593637998885918…58042260623966208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.710 Γ— 10⁹⁸(99-digit number)
57109187275997771837…16084521247932416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.142 Γ— 10⁹⁹(100-digit number)
11421837455199554367…32169042495864832001
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:57,969,687 XPMΒ·at block #6,840,667 Β· updates every 60s
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