Block #331,134

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/27/2013, 5:19:58 AM · Difficulty 10.1649 · 6,479,968 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5f7400c66502c6704c560505746138b86749f7964199f93f2813ce62910a8eb4

View on Chainz ↗

Height

#331,134

Difficulty

10.164935

Transactions

Size

1.04 KB

Version

Bits

0a2a3933

Nonce

187,516

Timestamp

12/27/2013, 5:19:58 AM

Confirmations

6,479,968

Mined by

AFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

49eb881d007426ce388e52587d90e2d4a548001cab8a74764c2d165f42a3668e

Transactions (1)

Coinbase49eb881d007426…2d165f42a3668e

1 in → 27 out9.6600 XPM981 B

AFutDVqJ…TJTJj6UF Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 Ad9pSzHt…cpJ3y2zz

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.

1.163 × 10⁹³(94-digit number)

11639129766539361352…93305321836187343999

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

1.163 × 10⁹³(94-digit number)

11639129766539361352…93305321836187343999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.327 × 10⁹³(94-digit number)

23278259533078722705…86610643672374687999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.655 × 10⁹³(94-digit number)

46556519066157445411…73221287344749375999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.311 × 10⁹³(94-digit number)

93113038132314890823…46442574689498751999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.862 × 10⁹⁴(95-digit number)

18622607626462978164…92885149378997503999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.724 × 10⁹⁴(95-digit number)

37245215252925956329…85770298757995007999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.449 × 10⁹⁴(95-digit number)

74490430505851912658…71540597515990015999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.489 × 10⁹⁵(96-digit number)

14898086101170382531…43081195031980031999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.979 × 10⁹⁵(96-digit number)

29796172202340765063…86162390063960063999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.959 × 10⁹⁵(96-digit number)

59592344404681530126…72324780127920127999

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 #331,134

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