Block #173,937

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/21/2013, 8:27:30 AM · Difficulty 9.8601 · 6,622,012 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

90dc50414f448b3ad5dd7d3225767aacec45c5d41e21a3cff6cb2e1c70a7c3dc

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Height

#173,937

Difficulty

9.860132

Transactions

Size

1013 B

Version

Bits

09dc319f

Nonce

17,445

Timestamp

9/21/2013, 8:27:30 AM

Confirmations

6,622,012

Mined by

⛏️ P2SHAUYP7xMhjtcNUrsYAvWCNJxfBCvJxk1Vap

Merkle Root

4d69691556a96e3fc8aaf67622428bea4af85797f1ca032f351dac9f95cff71d

Transactions (2)

Coinbase11978a0026b0f7…086a78a3fd42cb

1 in → 1 out10.2800 XPM109 B

AUYP7xMh…vJxk1Vap

a8cd9a5ba35556…01bc34a621120d

5 in → 2 out30.1787 XPM815 B

AZoTowvW…KJoS4PJA APfmBCjs…78YaNPMG

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.

2.665 × 10⁹³(94-digit number)

26651551398778052184…59906093218359028159

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

2.665 × 10⁹³(94-digit number)

26651551398778052184…59906093218359028159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.330 × 10⁹³(94-digit number)

53303102797556104368…19812186436718056319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.066 × 10⁹⁴(95-digit number)

10660620559511220873…39624372873436112639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.132 × 10⁹⁴(95-digit number)

21321241119022441747…79248745746872225279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.264 × 10⁹⁴(95-digit number)

42642482238044883494…58497491493744450559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.528 × 10⁹⁴(95-digit number)

85284964476089766989…16994982987488901119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.705 × 10⁹⁵(96-digit number)

17056992895217953397…33989965974977802239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.411 × 10⁹⁵(96-digit number)

34113985790435906795…67979931949955604479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.822 × 10⁹⁵(96-digit number)

68227971580871813591…35959863899911208959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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