Block #95,658

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/3/2013, 7:54:03 PM · Difficulty 9.2317 · 6,695,653 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

993857fac6ae9c056d6c21e0bc3e0c3c46888e8b574990e5d78bd8d11148de16

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Height

#95,658

Difficulty

9.231701

Transactions

Size

200 B

Version

Bits

093b50c0

Nonce

121,141

Timestamp

8/3/2013, 7:54:03 PM

Confirmations

6,695,653

Merkle Root

900ccde2183f2a230ce8783fffb6ba3674845be69f5c38e02bb6f9b11395e022

Transactions (1)

Coinbase900ccde2183f2a…b6f9b11395e022

1 in → 1 out11.7200 XPM109 B

AWuDuxGX…tLDpHWp7

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.

6.073 × 10⁹⁶(97-digit number)

60739526207813772026…66284197832772436631

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

6.073 × 10⁹⁶(97-digit number)

60739526207813772026…66284197832772436631

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.214 × 10⁹⁷(98-digit number)

12147905241562754405…32568395665544873261

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.429 × 10⁹⁷(98-digit number)

24295810483125508810…65136791331089746521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.859 × 10⁹⁷(98-digit number)

48591620966251017621…30273582662179493041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

9.718 × 10⁹⁷(98-digit number)

97183241932502035242…60547165324358986081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.943 × 10⁹⁸(99-digit number)

19436648386500407048…21094330648717972161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.887 × 10⁹⁸(99-digit number)

38873296773000814097…42188661297435944321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

7.774 × 10⁹⁸(99-digit number)

77746593546001628194…84377322594871888641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.554 × 10⁹⁹(100-digit number)

15549318709200325638…68754645189743777281

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