Block #90,268

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/31/2013, 12:02:03 AM · Difficulty 9.2479 · 6,704,018 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

4475b82e35d3249376655eea702a3e77a0bcbefac5fbc76988147e9c85a53405

View on Chainz ↗

Height

#90,268

Difficulty

9.247881

Transactions

Size

204 B

Version

Bits

093f7521

Nonce

6,303

Timestamp

7/31/2013, 12:02:03 AM

Confirmations

6,704,018

Merkle Root

af69a740ff60d519d90656b90c21ddd7bc85ac82259f66bc6a8a7c71cbad3bb2

Transactions (1)

Coinbaseaf69a740ff60d5…8a7c71cbad3bb2

1 in → 1 out11.6800 XPM109 B

AdhmaJ1p…MhFRDjQ7

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.

1.623 × 10¹⁰⁷(108-digit number)

16238745769328881745…07759869465768261641

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

1.623 × 10¹⁰⁷(108-digit number)

16238745769328881745…07759869465768261641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.247 × 10¹⁰⁷(108-digit number)

32477491538657763490…15519738931536523281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.495 × 10¹⁰⁷(108-digit number)

64954983077315526980…31039477863073046561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.299 × 10¹⁰⁸(109-digit number)

12990996615463105396…62078955726146093121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.598 × 10¹⁰⁸(109-digit number)

25981993230926210792…24157911452292186241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.196 × 10¹⁰⁸(109-digit number)

51963986461852421584…48315822904584372481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.039 × 10¹⁰⁹(110-digit number)

10392797292370484316…96631645809168744961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.078 × 10¹⁰⁹(110-digit number)

20785594584740968633…93263291618337489921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.157 × 10¹⁰⁹(110-digit number)

41571189169481937267…86526583236674979841

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