Block #479,086

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/7/2014, 11:53:29 AM · Difficulty 10.5002 · 6,324,520 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5fb416ded933afb372bba7c22d5cd31465420240dd100b5d3e2521691cb75485

View on Chainz ↗

Height

#479,086

Difficulty

10.500227

Transactions

Size

833 B

Version

Bits

0a800ede

Nonce

73,801

Timestamp

4/7/2014, 11:53:29 AM

Confirmations

6,324,520

Mined by

⛏️ nOaSBdAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

4336f37ea9df861f2023ff8fbb27afe86464002df8546c8c06833141c05399be

Transactions (1)

Coinbase4336f37ea9df86…833141c05399be

1 in → 20 out9.0600 XPM743 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ALqxX1WA…hsKjbnXn

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.

4.146 × 10⁹⁴(95-digit number)

41469638245552583177…59494619103171101399

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

4.146 × 10⁹⁴(95-digit number)

41469638245552583177…59494619103171101399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.293 × 10⁹⁴(95-digit number)

82939276491105166355…18989238206342202799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.658 × 10⁹⁵(96-digit number)

16587855298221033271…37978476412684405599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.317 × 10⁹⁵(96-digit number)

33175710596442066542…75956952825368811199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.635 × 10⁹⁵(96-digit number)

66351421192884133084…51913905650737622399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.327 × 10⁹⁶(97-digit number)

13270284238576826616…03827811301475244799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.654 × 10⁹⁶(97-digit number)

26540568477153653233…07655622602950489599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.308 × 10⁹⁶(97-digit number)

53081136954307306467…15311245205900979199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.061 × 10⁹⁷(98-digit number)

10616227390861461293…30622490411801958399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.123 × 10⁹⁷(98-digit number)

21232454781722922586…61244980823603916799

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