Block #25,948

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/13/2013, 3:49:11 AM · Difficulty 7.9731 · 6,770,447 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

773e692b63458bc64f4bd0413a1bf798b493b76be185298307c39c45ec2bbdd7

View on Chainz ↗

Height

#25,948

Difficulty

7.973127

Transactions

Size

1.42 KB

Version

Bits

07f91ee2

Nonce

1,183

Timestamp

7/13/2013, 3:49:11 AM

Confirmations

6,770,447

Mined by

⛏️ P2SHAMAsrnszMdk7D2xh8TKDhzb5Ai99mSq6AM

Merkle Root

21c64bfedb9ea5508f39a61d59662a35daf5c151b6f169e074ea9fade95cb33b

Transactions (2)

Coinbase6e9dea9ffc1973…3a41802418f0fb

1 in → 1 out15.7300 XPM108 B

AMAsrnsz…99mSq6AM

d9c45b7ce31f9b…09eefd8283b792

10 in → 1 out127.0000 XPM1.22 KB

AQVQQag1…hz1t6GJH

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.

9.036 × 10¹¹²(113-digit number)

90369677403336532874…05002994124560069399

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

9.036 × 10¹¹²(113-digit number)

90369677403336532874…05002994124560069399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.807 × 10¹¹³(114-digit number)

18073935480667306574…10005988249120138799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.614 × 10¹¹³(114-digit number)

36147870961334613149…20011976498240277599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.229 × 10¹¹³(114-digit number)

72295741922669226299…40023952996480555199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.445 × 10¹¹⁴(115-digit number)

14459148384533845259…80047905992961110399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.891 × 10¹¹⁴(115-digit number)

28918296769067690519…60095811985922220799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.783 × 10¹¹⁴(115-digit number)

57836593538135381039…20191623971844441599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.156 × 10¹¹⁵(116-digit number)

11567318707627076207…40383247943688883199

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer