Block #93,906

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/2/2013, 6:15:44 PM · Difficulty 9.1969 · 6,697,034 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

018e3ab803744dad841019a7cc90d2e22d2da17153784b3aa51b36b76175589f

View on Chainz ↗

Height

#93,906

Difficulty

9.196902

Transactions

Size

4.21 KB

Version

Bits

0932682b

Nonce

69,861

Timestamp

8/2/2013, 6:15:44 PM

Confirmations

6,697,034

Merkle Root

45837eab73c39f71f9a02de943df666cd65cca5cc6df4bf33f2a7b0ffed27572

Transactions (2)

Coinbase379e3c6175c36b…06bda55d252952

1 in → 1 out11.8600 XPM109 B

Ab7CGktC…E6BD22Zg

84d49383dcb66b…fcaf30f69a6b52

35 in → 2 out400.6405 XPM4.01 KB

AL3jCG2K…moye79K3 ASR7Uerm…gzYsZdMj

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.

7.389 × 10¹¹⁰(111-digit number)

73897312809708375352…11572459762342361581

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

7.389 × 10¹¹⁰(111-digit number)

73897312809708375352…11572459762342361581

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.477 × 10¹¹¹(112-digit number)

14779462561941675070…23144919524684723161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.955 × 10¹¹¹(112-digit number)

29558925123883350140…46289839049369446321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.911 × 10¹¹¹(112-digit number)

59117850247766700281…92579678098738892641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.182 × 10¹¹²(113-digit number)

11823570049553340056…85159356197477785281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.364 × 10¹¹²(113-digit number)

23647140099106680112…70318712394955570561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.729 × 10¹¹²(113-digit number)

47294280198213360225…40637424789911141121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.458 × 10¹¹²(113-digit number)

94588560396426720450…81274849579822282241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.891 × 10¹¹³(114-digit number)

18917712079285344090…62549699159644564481

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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