Block #446,946

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/16/2014, 10:16:09 PM · Difficulty 10.3608 · 6,358,798 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f0d4c354ec2009a5d22f68960f58aa0b8ddec1d8fc3d35a595ecb41513443d43

View on Chainz ↗

Height

#446,946

Difficulty

10.360776

Transactions

Size

1.01 KB

Version

Bits

0a5c5bc9

Nonce

207,538

Timestamp

3/16/2014, 10:16:09 PM

Confirmations

6,358,798

Mined by

⛏️ aS&"lAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

800ebb760a8ceacb56a7324a6326252cbb92223c51a0b3903928ca33de206aa9

Transactions (1)

Coinbase800ebb760a8cea…28ca33de206aa9

1 in → 26 out9.3000 XPM947 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AcV2etJ3…AC6C3Zed

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.

1.461 × 10⁹⁴(95-digit number)

14618319374963877466…29701724637390899199

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

1.461 × 10⁹⁴(95-digit number)

14618319374963877466…29701724637390899199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.923 × 10⁹⁴(95-digit number)

29236638749927754932…59403449274781798399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.847 × 10⁹⁴(95-digit number)

58473277499855509864…18806898549563596799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.169 × 10⁹⁵(96-digit number)

11694655499971101972…37613797099127193599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.338 × 10⁹⁵(96-digit number)

23389310999942203945…75227594198254387199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.677 × 10⁹⁵(96-digit number)

46778621999884407891…50455188396508774399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.355 × 10⁹⁵(96-digit number)

93557243999768815783…00910376793017548799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.871 × 10⁹⁶(97-digit number)

18711448799953763156…01820753586035097599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.742 × 10⁹⁶(97-digit number)

37422897599907526313…03641507172070195199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.484 × 10⁹⁶(97-digit number)

74845795199815052626…07283014344140390399

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