Block #478,958

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/7/2014, 10:00:12 AM · Difficulty 10.4984 · 6,326,107 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fbd1ab74aa6577a6ed1f4daeca33029047d6c5fe73fbe26618ccb790f5036cc9

View on Chainz ↗

Height

#478,958

Difficulty

10.498418

Transactions

Size

869 B

Version

Bits

0a7f985a

Nonce

11,254

Timestamp

4/7/2014, 10:00:12 AM

Confirmations

6,326,107

Mined by

⛏️ N~AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

da61984f2ac3732419b10c3dbed5604828d94e92054a51e3b435b0b9825f2a08

Transactions (1)

Coinbaseda61984f2ac373…35b0b9825f2a08

1 in → 21 out9.0600 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUzEPJFG…kYkA5U9V AZ34NcPy…8FPeFjPV Adbb4svj…dQWTHsq5

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.

1.559 × 10⁹⁹(100-digit number)

15592267451987656303…10919023855665433599

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

1.559 × 10⁹⁹(100-digit number)

15592267451987656303…10919023855665433599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.118 × 10⁹⁹(100-digit number)

31184534903975312607…21838047711330867199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.236 × 10⁹⁹(100-digit number)

62369069807950625214…43676095422661734399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.247 × 10¹⁰⁰(101-digit number)

12473813961590125042…87352190845323468799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.494 × 10¹⁰⁰(101-digit number)

24947627923180250085…74704381690646937599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.989 × 10¹⁰⁰(101-digit number)

49895255846360500171…49408763381293875199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.979 × 10¹⁰⁰(101-digit number)

99790511692721000343…98817526762587750399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.995 × 10¹⁰¹(102-digit number)

19958102338544200068…97635053525175500799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.991 × 10¹⁰¹(102-digit number)

39916204677088400137…95270107050351001599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.983 × 10¹⁰¹(102-digit number)

79832409354176800275…90540214100702003199

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