Block #446,323

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/16/2014, 11:44:46 AM · Difficulty 10.3604 · 6,380,508 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d4143eca8b11d93188040ccbc57021292155cf2ca6259e0e34e4529ba17e1d80

View on Chainz ↗

Height

#446,323

Difficulty

10.360430

Transactions

Size

1003 B

Version

Bits

0a5c4529

Nonce

241,645

Timestamp

3/16/2014, 11:44:46 AM

Confirmations

6,380,508

Mined by

⛏️ saS%~AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

0517b01d006f4f63db6cfe9a7b494e7ecec5a90a6dfcfabf11100be0ee3a2db4

Transactions (1)

Coinbase0517b01d006f4f…100be0ee3a2db4

1 in → 25 out9.3000 XPM913 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.

4.969 × 10⁹⁵(96-digit number)

49691666309341670077…78467338975070850559

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

4.969 × 10⁹⁵(96-digit number)

49691666309341670077…78467338975070850559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

9.938 × 10⁹⁵(96-digit number)

99383332618683340154…56934677950141701119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.987 × 10⁹⁶(97-digit number)

19876666523736668030…13869355900283402239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.975 × 10⁹⁶(97-digit number)

39753333047473336061…27738711800566804479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

7.950 × 10⁹⁶(97-digit number)

79506666094946672123…55477423601133608959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.590 × 10⁹⁷(98-digit number)

15901333218989334424…10954847202267217919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.180 × 10⁹⁷(98-digit number)

31802666437978668849…21909694404534435839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.360 × 10⁹⁷(98-digit number)

63605332875957337698…43819388809068871679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.272 × 10⁹⁸(99-digit number)

12721066575191467539…87638777618137743359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.544 × 10⁹⁸(99-digit number)

25442133150382935079…75277555236275486719

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 #446,323

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