Block #511,863

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/26/2014, 12:28:43 PM · Difficulty 10.8315 · 6,283,279 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f9239027a8aef963e6da6270c18026231dda3cdcc2e3da1cdd649c33b3945b4d

View on Chainz ↗

Height

#511,863

Difficulty

10.831501

Transactions

Size

208 B

Version

Bits

0ad4dd42

Nonce

49,255,670

Timestamp

4/26/2014, 12:28:43 PM

Confirmations

6,283,279

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c1ff486c6bb85ac7255bbc616f9b0c369de1c9a2ac444ed2a137952cc4335afd

Transactions (1)

Coinbasec1ff486c6bb85a…37952cc4335afd

1 in → 1 out8.5100 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.

2.308 × 10¹⁰⁰(101-digit number)

23084360940063335594…00719475355450880001

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

2.308 × 10¹⁰⁰(101-digit number)

23084360940063335594…00719475355450880001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.616 × 10¹⁰⁰(101-digit number)

46168721880126671189…01438950710901760001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.233 × 10¹⁰⁰(101-digit number)

92337443760253342379…02877901421803520001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.846 × 10¹⁰¹(102-digit number)

18467488752050668475…05755802843607040001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.693 × 10¹⁰¹(102-digit number)

36934977504101336951…11511605687214080001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.386 × 10¹⁰¹(102-digit number)

73869955008202673903…23023211374428160001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.477 × 10¹⁰²(103-digit number)

14773991001640534780…46046422748856320001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.954 × 10¹⁰²(103-digit number)

29547982003281069561…92092845497712640001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.909 × 10¹⁰²(103-digit number)

59095964006562139122…84185690995425280001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.181 × 10¹⁰³(104-digit number)

11819192801312427824…68371381990850560001

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