Block #95,633

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/3/2013, 7:28:39 PM · Difficulty 9.2318 · 6,729,784 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9ade67b8162c454ccf88a899728fa18e7451e0dcba92fa6a8ba1e27ff4fdd580

View on Chainz ↗

Height

#95,633

Difficulty

9.231753

Transactions

Size

206 B

Version

Bits

093b5430

Nonce

26,112

Timestamp

8/3/2013, 7:28:39 PM

Confirmations

6,729,784

Mined by

⛏️ P2SHAdqhSCkqzFK2H7qur7FeS9kZvqFJ93rsXN

Merkle Root

a328807c93ab8a5b9102891232b1195e7cc5ba1aaaf47d21caf671c2a0cc2d77

Transactions (1)

Coinbasea328807c93ab8a…f671c2a0cc2d77

1 in → 1 out11.7200 XPM109 B

AdqhSCkq…FJ93rsXN

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.

8.957 × 10¹¹⁰(111-digit number)

89570831666463530646…32807118585200023359

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

8.957 × 10¹¹⁰(111-digit number)

89570831666463530646…32807118585200023359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.791 × 10¹¹¹(112-digit number)

17914166333292706129…65614237170400046719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.582 × 10¹¹¹(112-digit number)

35828332666585412258…31228474340800093439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.165 × 10¹¹¹(112-digit number)

71656665333170824516…62456948681600186879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.433 × 10¹¹²(113-digit number)

14331333066634164903…24913897363200373759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.866 × 10¹¹²(113-digit number)

28662666133268329806…49827794726400747519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.732 × 10¹¹²(113-digit number)

57325332266536659613…99655589452801495039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.146 × 10¹¹³(114-digit number)

11465066453307331922…99311178905602990079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.293 × 10¹¹³(114-digit number)

22930132906614663845…98622357811205980159

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 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 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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #95,633

Cookie Preferences