Block #419,833

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/25/2014, 11:27:21 PM · Difficulty 10.3686 · 6,405,074 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

516626eed566bd3cc47aeb6da3fc083ac1f6a7257e99c98cb5d99aecc5e25851

View on Chainz ↗

Height

#419,833

Difficulty

10.368609

Transactions

Size

208 B

Version

Bits

0a5e5d2b

Nonce

3,060

Timestamp

2/25/2014, 11:27:21 PM

Confirmations

6,405,074

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

753b80cd8e720e169ffab0cad3d61731e5fabad583f3bbf32a4ec75cca9b6e61

Transactions (1)

Coinbase753b80cd8e720e…4ec75cca9b6e61

1 in → 1 out9.2900 XPM116 B

AbwWkWZt…kawDhufa

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.

6.904 × 10⁹⁹(100-digit number)

69048466646717487039…42089630013175875199

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

6.904 × 10⁹⁹(100-digit number)

69048466646717487039…42089630013175875199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.380 × 10¹⁰⁰(101-digit number)

13809693329343497407…84179260026351750399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.761 × 10¹⁰⁰(101-digit number)

27619386658686994815…68358520052703500799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.523 × 10¹⁰⁰(101-digit number)

55238773317373989631…36717040105407001599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.104 × 10¹⁰¹(102-digit number)

11047754663474797926…73434080210814003199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.209 × 10¹⁰¹(102-digit number)

22095509326949595852…46868160421628006399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.419 × 10¹⁰¹(102-digit number)

44191018653899191705…93736320843256012799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.838 × 10¹⁰¹(102-digit number)

88382037307798383411…87472641686512025599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.767 × 10¹⁰²(103-digit number)

17676407461559676682…74945283373024051199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.535 × 10¹⁰²(103-digit number)

35352814923119353364…49890566746048102399

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 First 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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #419,833

Cookie Preferences