Block #485,906

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/11/2014, 8:06:44 AM · Difficulty 10.6146 · 6,353,517 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

172823195e10d4ea63119dfd038d626a2d40166b7aac9755912c1e1457a8d437

View on Chainz ↗

Height

#485,906

Difficulty

10.614602

Transactions

Size

834 B

Version

Bits

0a9d5691

Nonce

7,765

Timestamp

4/11/2014, 8:06:44 AM

Confirmations

6,353,517

Mined by

⛏️ jaSG?AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d5c95978b77f7e05c17d6a5f9b54a1e310c6a6f359c9f35ea5d8889fcc5fd7ee

Transactions (1)

Coinbased5c95978b77f7e…d8889fcc5fd7ee

1 in → 20 out8.8597 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3 ATKK7iFz…wZm46KN1

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.

4.805 × 10⁹⁶(97-digit number)

48057889952863526065…74101971469800401919

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

4.805 × 10⁹⁶(97-digit number)

48057889952863526065…74101971469800401919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.611 × 10⁹⁶(97-digit number)

96115779905727052130…48203942939600803839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.922 × 10⁹⁷(98-digit number)

19223155981145410426…96407885879201607679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.844 × 10⁹⁷(98-digit number)

38446311962290820852…92815771758403215359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.689 × 10⁹⁷(98-digit number)

76892623924581641704…85631543516806430719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.537 × 10⁹⁸(99-digit number)

15378524784916328340…71263087033612861439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.075 × 10⁹⁸(99-digit number)

30757049569832656681…42526174067225722879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.151 × 10⁹⁸(99-digit number)

61514099139665313363…85052348134451445759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.230 × 10⁹⁹(100-digit number)

12302819827933062672…70104696268902891519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.460 × 10⁹⁹(100-digit number)

24605639655866125345…40209392537805783039

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

Block #485,906

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