Block #426,344

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/2/2014, 1:18:42 PM · Difficulty 10.3610 · 6,376,188 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e962cf2795d9e6a37104e583f9d040de45f4a7d761e8a0a374ac837df547e01b

View on Chainz ↗

Height

#426,344

Difficulty

10.361024

Transactions

Size

967 B

Version

Bits

0a5c6c0e

Nonce

185,235

Timestamp

3/2/2014, 1:18:42 PM

Confirmations

6,376,188

Mined by

⛏️ haSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e08e205ad5e2827683d8f441611dc485e352ad246d5b24ff4b72b0c3f1328c2b

Transactions (1)

Coinbasee08e205ad5e282…72b0c3f1328c2b

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

6.377 × 10⁹⁰(91-digit number)

63770367318552467483…15799368704238288899

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

6.377 × 10⁹⁰(91-digit number)

63770367318552467483…15799368704238288899

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.275 × 10⁹¹(92-digit number)

12754073463710493496…31598737408476577799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.550 × 10⁹¹(92-digit number)

25508146927420986993…63197474816953155599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.101 × 10⁹¹(92-digit number)

51016293854841973986…26394949633906311199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.020 × 10⁹²(93-digit number)

10203258770968394797…52789899267812622399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.040 × 10⁹²(93-digit number)

20406517541936789594…05579798535625244799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.081 × 10⁹²(93-digit number)

40813035083873579189…11159597071250489599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

8.162 × 10⁹²(93-digit number)

81626070167747158378…22319194142500979199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.632 × 10⁹³(94-digit number)

16325214033549431675…44638388285001958399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

3.265 × 10⁹³(94-digit number)

32650428067098863351…89276776570003916799

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