Block #186,228

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/29/2013, 7:13:41 PM · Difficulty 9.8647 · 6,610,658 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c1c7ad94e12f49b20b92e88f60f186345305ccd5b0721de28e48e85adad63365

View on Chainz ↗

Height

#186,228

Difficulty

9.864696

Transactions

Size

1.51 KB

Version

Bits

09dd5cb0

Nonce

1,164,815,953

Timestamp

9/29/2013, 7:13:41 PM

Confirmations

6,610,658

Mined by

⛏️ tRH{AJYYHSv7evqm2NrAu8V9H7ymBQkiK98usT

Merkle Root

d8d37b7fe3c6871eca69f4116cb075ca188f63e2802d0212425a4bc68a7f1d51

Transactions (1)

Coinbased8d37b7fe3c687…5a4bc68a7f1d51

1 in → 41 out10.2500 XPM1.42 KB

AJYYHSv7…kiK98usT AGB4r7xv…BBsSHL1w APxhhWVB…fH2xP7H4 AV4rziFj…QhTLsLyZ AL7194fk…YNQBVjTB

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.

2.255 × 10⁹⁷(98-digit number)

22551900994447081321…63240271623892505601

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

2.255 × 10⁹⁷(98-digit number)

22551900994447081321…63240271623892505601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.510 × 10⁹⁷(98-digit number)

45103801988894162643…26480543247785011201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.020 × 10⁹⁷(98-digit number)

90207603977788325286…52961086495570022401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.804 × 10⁹⁸(99-digit number)

18041520795557665057…05922172991140044801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.608 × 10⁹⁸(99-digit number)

36083041591115330114…11844345982280089601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.216 × 10⁹⁸(99-digit number)

72166083182230660228…23688691964560179201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.443 × 10⁹⁹(100-digit number)

14433216636446132045…47377383929120358401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.886 × 10⁹⁹(100-digit number)

28866433272892264091…94754767858240716801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.773 × 10⁹⁹(100-digit number)

57732866545784528183…89509535716481433601

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer