Block #445,840

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/16/2014, 4:01:58 AM · Difficulty 10.3590 · 6,380,206 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

77ee618112f68157bf5b8dc0de134135af8090e71da98214a7bbe5b62d1269b4

View on Chainz ↗

Height

#445,840

Difficulty

10.358984

Transactions

Size

1002 B

Version

Bits

0a5be668

Nonce

4,038

Timestamp

3/16/2014, 4:01:58 AM

Confirmations

6,380,206

Mined by

⛏️ aS%"7AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f5f0e8bd7b547178d2d4441fa698c7b006d004aadd8dc330d89d91a24b80020a

Transactions (1)

Coinbasef5f0e8bd7b5471…9d91a24b80020a

1 in → 25 out9.3000 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn 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.

2.521 × 10⁹³(94-digit number)

25212693309251510993…75671507070201508479

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

2.521 × 10⁹³(94-digit number)

25212693309251510993…75671507070201508479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.042 × 10⁹³(94-digit number)

50425386618503021986…51343014140403016959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.008 × 10⁹⁴(95-digit number)

10085077323700604397…02686028280806033919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.017 × 10⁹⁴(95-digit number)

20170154647401208794…05372056561612067839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.034 × 10⁹⁴(95-digit number)

40340309294802417589…10744113123224135679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.068 × 10⁹⁴(95-digit number)

80680618589604835178…21488226246448271359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.613 × 10⁹⁵(96-digit number)

16136123717920967035…42976452492896542719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.227 × 10⁹⁵(96-digit number)

32272247435841934071…85952904985793085439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.454 × 10⁹⁵(96-digit number)

64544494871683868142…71905809971586170879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.290 × 10⁹⁶(97-digit number)

12908898974336773628…43811619943172341759

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 #445,840

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