Block #287,168

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/1/2013, 5:13:11 AM · Difficulty 9.9864 · 6,507,450 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b41743628082aee291c14fa7c9dd313be03549f2265f740a491bd496e28ec04d

View on Chainz ↗

Height

#287,168

Difficulty

9.986378

Transactions

Size

829 B

Version

Bits

09fc8347

Nonce

208,204

Timestamp

12/1/2013, 5:13:11 AM

Confirmations

6,507,450

Mined by

⛏️ aaR#AGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

cafd46edbe03ddf25d601cc722a03f1a6a38bf98c618aa8bcfe408cd581004fb

Transactions (1)

Coinbasecafd46edbe03dd…e408cd581004fb

1 in → 20 out10.0100 XPM742 B

AGFAJ5YL…ZEnBbk6G AYcLTeXR…bscgPops AYrgZtF4…6oLCC7XK AVKFC9nD…J9zTymTX ASPzomex…JkjSwA1z

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.

9.821 × 10⁸⁷(88-digit number)

98213356053449379131…94953207229854371999

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

9.821 × 10⁸⁷(88-digit number)

98213356053449379131…94953207229854371999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.964 × 10⁸⁸(89-digit number)

19642671210689875826…89906414459708743999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.928 × 10⁸⁸(89-digit number)

39285342421379751652…79812828919417487999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.857 × 10⁸⁸(89-digit number)

78570684842759503305…59625657838834975999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.571 × 10⁸⁹(90-digit number)

15714136968551900661…19251315677669951999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.142 × 10⁸⁹(90-digit number)

31428273937103801322…38502631355339903999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.285 × 10⁸⁹(90-digit number)

62856547874207602644…77005262710679807999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.257 × 10⁹⁰(91-digit number)

12571309574841520528…54010525421359615999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.514 × 10⁹⁰(91-digit number)

25142619149683041057…08021050842719231999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.028 × 10⁹⁰(91-digit number)

50285238299366082115…16042101685438463999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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