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Block #381,487

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/30/2014, 1:02:19 AM Β· Difficulty 10.4052 Β· 6,415,033 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4c54f32ff227ad946b8e163e472756f6b4b27fef8254fad2bcf69f9242d6fe30
View on Chainz β†—

Height

#381,487

Difficulty

10.405229

Transactions

2

Size

575 B

Version

2

Bits

0a67bd13

Nonce

79,333

Timestamp

1/30/2014, 1:02:19 AM

Confirmations

6,415,033

Mined by

⛏️ oAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

802c1995f91311668f973648bff68b32f8bc3bfe31df426313c9d8029efd82ad
Transactions (2)
Coinbasecfa046ab8751f4…19b5fd71a949cd
1 in β†’ 1 out9.2300 XPM110 B
AeKNrjNj…1NEq95Ta
3c6bc0a17a5390…e8313815128f47
2 in β†’ 2 out289.5644 XPM374 B
AQP8BpEs…51PVfoAtAU8pQYSS…6AfDf3hS
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.

2.276 Γ— 10⁹⁢(97-digit number)
22765446103707719021…94169857406598846081
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
2.276 Γ— 10⁹⁢(97-digit number)
22765446103707719021…94169857406598846081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.553 Γ— 10⁹⁢(97-digit number)
45530892207415438042…88339714813197692161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.106 Γ— 10⁹⁢(97-digit number)
91061784414830876085…76679429626395384321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.821 Γ— 10⁹⁷(98-digit number)
18212356882966175217…53358859252790768641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.642 Γ— 10⁹⁷(98-digit number)
36424713765932350434…06717718505581537281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.284 Γ— 10⁹⁷(98-digit number)
72849427531864700868…13435437011163074561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.456 Γ— 10⁹⁸(99-digit number)
14569885506372940173…26870874022326149121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.913 Γ— 10⁹⁸(99-digit number)
29139771012745880347…53741748044652298241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.827 Γ— 10⁹⁸(99-digit number)
58279542025491760694…07483496089304596481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.165 Γ— 10⁹⁹(100-digit number)
11655908405098352138…14966992178609192961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.331 Γ— 10⁹⁹(100-digit number)
23311816810196704277…29933984357218385921
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:57,616,157 XPMΒ·at block #6,796,519 Β· updates every 60s
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