Block #26,303

2CCLength 8★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/13/2013, 4:56:10 AM · Difficulty 7.9746 · 6,764,981 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e5e0bd3731cfb57239de7bba2f96a42b2dafeb13038f430da3597ce0f190af67

View on Chainz ↗

Height

#26,303

Difficulty

7.974629

Transactions

Size

869 B

Version

Bits

07f9814a

Nonce

1,521

Timestamp

7/13/2013, 4:56:10 AM

Confirmations

6,764,981

Merkle Root

c550cd2a779f85164204f80aaf2824bb31751f2d3ba66d171020ec15b21e0534

Transactions (2)

Coinbase73f4e074bccdec…f088fe3862d942

1 in → 1 out15.7100 XPM108 B

AMQZDEDc…8yuMT81x

9360b061ae531e…d38f88e4186cf7

4 in → 2 out999.9200 XPM671 B

APBVxsMT…RAhyERWU APPnY6AH…j5xgosu2

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.

1.566 × 10⁹⁴(95-digit number)

15664042065863231871…24668486827149935751

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

1.566 × 10⁹⁴(95-digit number)

15664042065863231871…24668486827149935751

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.132 × 10⁹⁴(95-digit number)

31328084131726463742…49336973654299871501

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.265 × 10⁹⁴(95-digit number)

62656168263452927484…98673947308599743001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.253 × 10⁹⁵(96-digit number)

12531233652690585496…97347894617199486001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.506 × 10⁹⁵(96-digit number)

25062467305381170993…94695789234398972001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.012 × 10⁹⁵(96-digit number)

50124934610762341987…89391578468797944001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.002 × 10⁹⁶(97-digit number)

10024986922152468397…78783156937595888001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.004 × 10⁹⁶(97-digit number)

20049973844304936795…57566313875191776001

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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