Block #289,421

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/2/2013, 4:57:37 AM · Difficulty 9.9885 · 6,506,650 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

755340cd8b2fef9b0f099d73ce620f5aef0d7a6a1cbb898eedf346717fffed2b

View on Chainz ↗

Height

#289,421

Difficulty

9.988511

Transactions

Size

1003 B

Version

Bits

09fd0f09

Nonce

22,597

Timestamp

12/2/2013, 4:57:37 AM

Confirmations

6,506,650

Mined by

⛏️ jaR6AYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

3802724524efa5029309cb6273decd7b8018b2d9be36b8b2852bf5e7a60f0727

Transactions (1)

Coinbase3802724524efa5…2bf5e7a60f0727

1 in → 25 out10.0100 XPM913 B

AYcLTeXR…bscgPops Ac6mGvmQ…XqWmPHjR Ae58nAEb…GFUA15fv Ad9pSzHt…cpJ3y2zz APFsQ3Fo…xoFKrF12

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.

2.380 × 10⁹⁴(95-digit number)

23800544726023480229…31293825447629785599

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

2.380 × 10⁹⁴(95-digit number)

23800544726023480229…31293825447629785599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.760 × 10⁹⁴(95-digit number)

47601089452046960458…62587650895259571199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.520 × 10⁹⁴(95-digit number)

95202178904093920917…25175301790519142399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.904 × 10⁹⁵(96-digit number)

19040435780818784183…50350603581038284799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.808 × 10⁹⁵(96-digit number)

38080871561637568366…00701207162076569599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.616 × 10⁹⁵(96-digit number)

76161743123275136733…01402414324153139199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.523 × 10⁹⁶(97-digit number)

15232348624655027346…02804828648306278399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.046 × 10⁹⁶(97-digit number)

30464697249310054693…05609657296612556799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.092 × 10⁹⁶(97-digit number)

60929394498620109387…11219314593225113599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.218 × 10⁹⁷(98-digit number)

12185878899724021877…22438629186450227199

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