Block #654,122

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/30/2014, 12:04:23 AM · Difficulty 10.9552 · 6,137,598 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

554045cf9931e25d79c6f75813d9baf82aa14390b872c0add766d75e9247c9b7

View on Chainz ↗

Height

#654,122

Difficulty

10.955186

Transactions

Size

69.37 KB

Version

Bits

0af4870b

Nonce

516,543,884

Timestamp

7/30/2014, 12:04:23 AM

Confirmations

6,137,598

Merkle Root

ac51f615f73d02531368a1706ac44a939bcf9ed2c9f04402f5fd0d846130f22b

Transactions (2)

Coinbase061f863a3931b7…6cde5ee83cffa1

1 in → 1 out9.0300 XPM116 B

ANSXnLY2…Sd25TjkD

e381861fd6de3e…658b1318f04eb6

478 in → 2 out500.0100 XPM69.16 KB

AW1MnTRV…hMbbvjSA AUE5QneS…bDZqwQ1J

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.174 × 10⁹⁷(98-digit number)

11740830053594504481…21672314177373880321

Discovered Prime Numbers

p_k = 2^k × 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.

origin + 1

1.174 × 10⁹⁷(98-digit number)

11740830053594504481…21672314177373880321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.348 × 10⁹⁷(98-digit number)

23481660107189008963…43344628354747760641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.696 × 10⁹⁷(98-digit number)

46963320214378017927…86689256709495521281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.392 × 10⁹⁷(98-digit number)

93926640428756035855…73378513418991042561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.878 × 10⁹⁸(99-digit number)

18785328085751207171…46757026837982085121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.757 × 10⁹⁸(99-digit number)

37570656171502414342…93514053675964170241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.514 × 10⁹⁸(99-digit number)

75141312343004828684…87028107351928340481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.502 × 10⁹⁹(100-digit number)

15028262468600965736…74056214703856680961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.005 × 10⁹⁹(100-digit number)

30056524937201931473…48112429407713361921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.011 × 10⁹⁹(100-digit number)

60113049874403862947…96224858815426723841

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer