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Block #2,647,380

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 9:43:39 PM Β· Difficulty 11.7585 Β· 4,191,198 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
89e581a3c4a96cf944379251deeab4bc1e49e054b76538f8d2d0027114449d92
View on Chainz β†—

Height

#2,647,380

Difficulty

11.758500

Transactions

1

Size

201 B

Version

2

Bits

0bc22d15

Nonce

1,142,691,192

Timestamp

5/3/2018, 9:43:39 PM

Confirmations

4,191,198

Mined by

⛏️ P2SHAdBxniUseWprWRHhU5odLXt9mf2mpc79LK

Merkle Root

c29cd0da2e5b1cb60e39b8fdcdb09ef92573dd4ff97c1d5d755420774f3499a8
Transactions (1)
Coinbasec29cd0da2e5b1c…5420774f3499a8
1 in β†’ 1 out7.2200 XPM110 B
AdBxniUs…2mpc79LK
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.

1.416 Γ— 10⁹⁷(98-digit number)
14163121187854550398…76030418435281715201
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
1.416 Γ— 10⁹⁷(98-digit number)
14163121187854550398…76030418435281715201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.832 Γ— 10⁹⁷(98-digit number)
28326242375709100797…52060836870563430401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.665 Γ— 10⁹⁷(98-digit number)
56652484751418201594…04121673741126860801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.133 Γ— 10⁹⁸(99-digit number)
11330496950283640318…08243347482253721601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.266 Γ— 10⁹⁸(99-digit number)
22660993900567280637…16486694964507443201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.532 Γ— 10⁹⁸(99-digit number)
45321987801134561275…32973389929014886401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.064 Γ— 10⁹⁸(99-digit number)
90643975602269122551…65946779858029772801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.812 Γ— 10⁹⁹(100-digit number)
18128795120453824510…31893559716059545601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.625 Γ— 10⁹⁹(100-digit number)
36257590240907649020…63787119432119091201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.251 Γ— 10⁹⁹(100-digit number)
72515180481815298041…27574238864238182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.450 Γ— 10¹⁰⁰(101-digit number)
14503036096363059608…55148477728476364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
2.900 Γ— 10¹⁰⁰(101-digit number)
29006072192726119216…10296955456952729601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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
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