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Block #476,175

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/5/2014, 4:12:03 PM Β· Difficulty 10.4698 Β· 6,319,716 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
daeb4e3559f29a94e51ca0a48f5d6093334872e4c0c36a37990b3665d785c4d5
View on Chainz β†—

Height

#476,175

Difficulty

10.469763

Transactions

1

Size

187 B

Version

2

Bits

0a78425d

Nonce

33,242

Timestamp

4/5/2014, 4:12:03 PM

Confirmations

6,319,716

Mined by

⛏️ DaS@+@lAYCeLhqBJ84jFrKumsmd4mf6paeqGM6KK1

Merkle Root

c9c86e139545b2e11819cca4a6dbcc50e54bb3c832d2096f1180c59dc41d2619
Transactions (1)
Coinbasec9c86e139545b2…80c59dc41d2619
1 in β†’ 1 out9.1100 XPM97 B
AYCeLhqB…eqGM6KK1
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.

5.013 Γ— 10⁹⁴(95-digit number)
50130628823474531896…17403805158205701121
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
5.013 Γ— 10⁹⁴(95-digit number)
50130628823474531896…17403805158205701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.002 Γ— 10⁹⁡(96-digit number)
10026125764694906379…34807610316411402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.005 Γ— 10⁹⁡(96-digit number)
20052251529389812758…69615220632822804481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.010 Γ— 10⁹⁡(96-digit number)
40104503058779625517…39230441265645608961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.020 Γ— 10⁹⁡(96-digit number)
80209006117559251034…78460882531291217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.604 Γ— 10⁹⁢(97-digit number)
16041801223511850206…56921765062582435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.208 Γ— 10⁹⁢(97-digit number)
32083602447023700413…13843530125164871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.416 Γ— 10⁹⁢(97-digit number)
64167204894047400827…27687060250329743361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.283 Γ— 10⁹⁷(98-digit number)
12833440978809480165…55374120500659486721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.566 Γ— 10⁹⁷(98-digit number)
25666881957618960330…10748241001318973441
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:57,611,212 XPMΒ·at block #6,795,890 Β· updates every 60s
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