Block #292,855

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/3/2013, 11:49:56 PM · Difficulty 9.9904 · 6,524,150 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

91784f831d924b3533d58064f301d71ba0bf95da3313bfa59c2ffca9b318e990

View on Chainz ↗

Height

#292,855

Difficulty

9.990419

Transactions

Size

1.14 KB

Version

Bits

09fd8c1b

Nonce

60,009

Timestamp

12/3/2013, 11:49:56 PM

Confirmations

6,524,150

Mined by

⛏️ waRngAZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

adfeb2ba799ededd6ba2bb29ba41e892e2d100c80c2d1a076f888d4c56ec3ad7

Transactions (1)

Coinbaseadfeb2ba799ede…888d4c56ec3ad7

1 in → 30 out9.9800 XPM1.06 KB

AZninDSu…FvgDMwC4 Ad9pSzHt…cpJ3y2zz AGmDpQMh…8qfUtstd APZoG4ZW…MqYepZby AMEghNXg…Egsrd3io

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.

2.256 × 10⁹³(94-digit number)

22560438842109467241…08992036076828154709

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

2.256 × 10⁹³(94-digit number)

22560438842109467241…08992036076828154709

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.512 × 10⁹³(94-digit number)

45120877684218934482…17984072153656309419

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.024 × 10⁹³(94-digit number)

90241755368437868964…35968144307312618839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.804 × 10⁹⁴(95-digit number)

18048351073687573792…71936288614625237679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.609 × 10⁹⁴(95-digit number)

36096702147375147585…43872577229250475359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.219 × 10⁹⁴(95-digit number)

72193404294750295171…87745154458500950719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.443 × 10⁹⁵(96-digit number)

14438680858950059034…75490308917001901439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.887 × 10⁹⁵(96-digit number)

28877361717900118068…50980617834003802879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.775 × 10⁹⁵(96-digit number)

57754723435800236137…01961235668007605759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.155 × 10⁹⁶(97-digit number)

11550944687160047227…03922471336015211519

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 #292,855

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