Block #445,910

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/16/2014, 5:12:24 AM · Difficulty 10.3588 · 6,363,539 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0060b93615467866a9ffbf50f7defebf3b0b6c9460cef8b5401bd28920da62b6

View on Chainz ↗

Height

#445,910

Difficulty

10.358788

Transactions

Size

731 B

Version

Bits

0a5bd981

Nonce

4,162

Timestamp

3/16/2014, 5:12:24 AM

Confirmations

6,363,539

Mined by

⛏️ aS%26AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

27853f43c2bf3b8505267c3bcfeaec6ec7aafc476dd1d22f663c8e1521b81b92

Transactions (1)

Coinbase27853f43c2bf3b…3c8e1521b81b92

1 in → 17 out9.3000 XPM641 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

5.180 × 10⁹³(94-digit number)

51803333797152905064…92009491970860479999

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

5.180 × 10⁹³(94-digit number)

51803333797152905064…92009491970860479999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.036 × 10⁹⁴(95-digit number)

10360666759430581012…84018983941720959999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.072 × 10⁹⁴(95-digit number)

20721333518861162025…68037967883441919999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.144 × 10⁹⁴(95-digit number)

41442667037722324051…36075935766883839999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.288 × 10⁹⁴(95-digit number)

82885334075444648103…72151871533767679999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.657 × 10⁹⁵(96-digit number)

16577066815088929620…44303743067535359999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.315 × 10⁹⁵(96-digit number)

33154133630177859241…88607486135070719999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.630 × 10⁹⁵(96-digit number)

66308267260355718483…77214972270141439999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.326 × 10⁹⁶(97-digit number)

13261653452071143696…54429944540282879999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.652 × 10⁹⁶(97-digit number)

26523306904142287393…08859889080565759999

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 #445,910

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