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Block #2,646,548

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/3/2018, 10:19:56 AM Β· Difficulty 11.7512 Β· 4,196,179 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ee136b53e0b3a47be4dc3a8710c9bd04f5a8d83eb51760b0b3e1a367a9c2a91
View on Chainz β†—

Height

#2,646,548

Difficulty

11.751232

Transactions

1

Size

201 B

Version

2

Bits

0bc050c1

Nonce

931,805,179

Timestamp

5/3/2018, 10:19:56 AM

Confirmations

4,196,179

Mined by

⛏️ P2SHASJYQdjf1cS99gouSrRXo3tefJKHaNiWUU

Merkle Root

7085acc3da92290b0f69deb8265e4c9ce73fa3ea44918a077c89163d61929993
Transactions (1)
Coinbase7085acc3da9229…89163d61929993
1 in β†’ 1 out7.2300 XPM110 B
ASJYQdjf…KHaNiWUU
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.

4.271 Γ— 10⁹⁷(98-digit number)
42710459217169671308…57251069208470712321
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
4.271 Γ— 10⁹⁷(98-digit number)
42710459217169671308…57251069208470712321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.542 Γ— 10⁹⁷(98-digit number)
85420918434339342616…14502138416941424641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.708 Γ— 10⁹⁸(99-digit number)
17084183686867868523…29004276833882849281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.416 Γ— 10⁹⁸(99-digit number)
34168367373735737046…58008553667765698561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.833 Γ— 10⁹⁸(99-digit number)
68336734747471474093…16017107335531397121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.366 Γ— 10⁹⁹(100-digit number)
13667346949494294818…32034214671062794241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.733 Γ— 10⁹⁹(100-digit number)
27334693898988589637…64068429342125588481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.466 Γ— 10⁹⁹(100-digit number)
54669387797977179274…28136858684251176961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.093 Γ— 10¹⁰⁰(101-digit number)
10933877559595435854…56273717368502353921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.186 Γ— 10¹⁰⁰(101-digit number)
21867755119190871709…12547434737004707841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
4.373 Γ— 10¹⁰⁰(101-digit number)
43735510238381743419…25094869474009415681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,986,155 XPMΒ·at block #6,842,726 Β· updates every 60s
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