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Block #41,567

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 4:52:35 PM Β· Difficulty 8.5353 Β· 6,755,307 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
45c6e707207f2369985a83dd0f43b245f57233f5db343ccae9c672209a081da4
View on Chainz β†—

Height

#41,567

Difficulty

8.535327

Transactions

2

Size

3.01 KB

Version

2

Bits

08890b2a

Nonce

86

Timestamp

7/14/2013, 4:52:35 PM

Confirmations

6,755,307

Mined by

⛏️ P2SHAcz8aGVgQtomPv8VR1HBsHZ8EFJhGrr8ay

Merkle Root

dabb62ef02357bdaa9d430b9cbc4ca5ea749bcffca8faaed90c6a9cc269892df
Transactions (2)
Coinbase937d7f5d121b2f…3d8d046c087d88
1 in β†’ 1 out13.7400 XPM109 B
Acz8aGVg…JhGrr8ay
dc1d128b7ea497…38665ee0c3f351
24 in β†’ 1 out320.4700 XPM2.81 KB
AWThhUX5…uhd1H2jp
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.

6.503 Γ— 10⁹⁡(96-digit number)
65038793924299719816…54325043640665735061
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
6.503 Γ— 10⁹⁡(96-digit number)
65038793924299719816…54325043640665735061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.300 Γ— 10⁹⁢(97-digit number)
13007758784859943963…08650087281331470121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.601 Γ— 10⁹⁢(97-digit number)
26015517569719887926…17300174562662940241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.203 Γ— 10⁹⁢(97-digit number)
52031035139439775853…34600349125325880481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.040 Γ— 10⁹⁷(98-digit number)
10406207027887955170…69200698250651760961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.081 Γ— 10⁹⁷(98-digit number)
20812414055775910341…38401396501303521921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.162 Γ— 10⁹⁷(98-digit number)
41624828111551820682…76802793002607043841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.324 Γ— 10⁹⁷(98-digit number)
83249656223103641364…53605586005214087681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,619,008 XPMΒ·at block #6,796,873 Β· updates every 60s
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