Block #177,844

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/23/2013, 11:13:59 PM · Difficulty 9.8642 · 6,614,992 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

0c7caddee224c0b634d2fd66003dd315a3fd49cdb68a904af970740f72fef41f

View on Chainz ↗

Height

#177,844

Difficulty

9.864153

Transactions

Size

197 B

Version

Bits

09dd391f

Nonce

8,490

Timestamp

9/23/2013, 11:13:59 PM

Confirmations

6,614,992

Merkle Root

97a7c1ce7cb4cdcccee8480edce4521af29bc841ff78920b75b700ecb8eea19a

Transactions (1)

Coinbase97a7c1ce7cb4cd…b700ecb8eea19a

1 in → 1 out10.2600 XPM109 B

AWsEijaA…9WbDL6tH

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.

2.800 × 10⁸⁹(90-digit number)

28007858960544208887…35518727720199451199

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

2.800 × 10⁸⁹(90-digit number)

28007858960544208887…35518727720199451199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.601 × 10⁸⁹(90-digit number)

56015717921088417774…71037455440398902399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.120 × 10⁹⁰(91-digit number)

11203143584217683554…42074910880797804799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.240 × 10⁹⁰(91-digit number)

22406287168435367109…84149821761595609599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.481 × 10⁹⁰(91-digit number)

44812574336870734219…68299643523191219199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.962 × 10⁹⁰(91-digit number)

89625148673741468439…36599287046382438399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.792 × 10⁹¹(92-digit number)

17925029734748293687…73198574092764876799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.585 × 10⁹¹(92-digit number)

35850059469496587375…46397148185529753599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.170 × 10⁹¹(92-digit number)

71700118938993174751…92794296371059507199

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