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Block #2,291,115

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2017, 8:45:46 PM Β· Difficulty 10.9550 Β· 4,552,478 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
40c4591de6b741ece8de3c4cc3d1906219f2c4bff47baf72b824b70d3cf44ad7
View on Chainz β†—

Height

#2,291,115

Difficulty

10.955013

Transactions

1

Size

199 B

Version

2

Bits

0af47bb3

Nonce

1,054,496,032

Timestamp

9/10/2017, 8:45:46 PM

Confirmations

4,552,478

Mined by

⛏️ P2SHAJZ9ge5KEcrcQecNSHbkAAnK5dXwsG4mX1

Merkle Root

33c2ed5e0f51fa06a2a57c34df67518d38de7e8f40261a6e94a5bc4bc66d6cb6
Transactions (1)
Coinbase33c2ed5e0f51fa…a5bc4bc66d6cb6
1 in β†’ 1 out8.3200 XPM109 B
AJZ9ge5K…XwsG4mX1
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.

2.528 Γ— 10⁹⁡(96-digit number)
25285240802634892450…93206016327524299201
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
2.528 Γ— 10⁹⁡(96-digit number)
25285240802634892450…93206016327524299201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.057 Γ— 10⁹⁡(96-digit number)
50570481605269784901…86412032655048598401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.011 Γ— 10⁹⁢(97-digit number)
10114096321053956980…72824065310097196801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.022 Γ— 10⁹⁢(97-digit number)
20228192642107913960…45648130620194393601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.045 Γ— 10⁹⁢(97-digit number)
40456385284215827921…91296261240388787201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.091 Γ— 10⁹⁢(97-digit number)
80912770568431655842…82592522480777574401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.618 Γ— 10⁹⁷(98-digit number)
16182554113686331168…65185044961555148801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.236 Γ— 10⁹⁷(98-digit number)
32365108227372662337…30370089923110297601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.473 Γ— 10⁹⁷(98-digit number)
64730216454745324674…60740179846220595201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.294 Γ— 10⁹⁸(99-digit number)
12946043290949064934…21480359692441190401
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:57,993,105 XPMΒ·at block #6,843,592 Β· updates every 60s
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