Block #448,848

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/18/2014, 5:43:23 AM · Difficulty 10.3641 · 6,355,054 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9c903a9148235e4f40f89f8c103a1cf5491c23d71a33d69feab6e5e7f2fbcee8

View on Chainz ↗

Height

#448,848

Difficulty

10.364132

Transactions

Size

968 B

Version

Bits

0a5d37bd

Nonce

51,587

Timestamp

3/18/2014, 5:43:23 AM

Confirmations

6,355,054

Mined by

⛏️ PaS'AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

852c39f36939dce1497dd22e7456fd4bd4c57aeb05792de9d52d2b26d0d2e0a7

Transactions (1)

Coinbase852c39f36939dc…2d2b26d0d2e0a7

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 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.

1.900 × 10⁹²(93-digit number)

19005454986476808236…12372587674748958719

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

1.900 × 10⁹²(93-digit number)

19005454986476808236…12372587674748958719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.801 × 10⁹²(93-digit number)

38010909972953616473…24745175349497917439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.602 × 10⁹²(93-digit number)

76021819945907232947…49490350698995834879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.520 × 10⁹³(94-digit number)

15204363989181446589…98980701397991669759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.040 × 10⁹³(94-digit number)

30408727978362893179…97961402795983339519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.081 × 10⁹³(94-digit number)

60817455956725786358…95922805591966679039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.216 × 10⁹⁴(95-digit number)

12163491191345157271…91845611183933358079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.432 × 10⁹⁴(95-digit number)

24326982382690314543…83691222367866716159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.865 × 10⁹⁴(95-digit number)

48653964765380629086…67382444735733432319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.730 × 10⁹⁴(95-digit number)

97307929530761258173…34764889471466864639

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