Block #214,395

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/17/2013, 11:26:47 AM · Difficulty 9.9231 · 6,577,434 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4c6f9fc28fb77cfe38ec2a3b31ed15983e1b689d404f6ec5bde7b794b7523fd0

View on Chainz ↗

Height

#214,395

Difficulty

9.923122

Transactions

Size

4.95 KB

Version

Bits

09ec51c0

Nonce

1,164,746,606

Timestamp

10/17/2013, 11:26:47 AM

Confirmations

6,577,434

Merkle Root

d1dfe5d67078c2225db5b6b74c62f55ecdf2b34830eae459d3376ba2b7d7634c

Transactions (2)

Coinbase8083c276491978…5ec312058487c2

1 in → 139 out10.0842 XPM4.68 KB

APui4t7L…pz97NdcB AGT9hnPx…C3sxd5B5 AehSbrXS…x2Vu99iu AWJHU8CF…JUjqyNaX AKtK4SH7…Ti8JpB2W

b5ce0e679c127f…332cb7861d9903

1 in → 2 out10.1500 XPM191 B

AQAvQSWZ…C9mFkvux AcsixBRe…rdAAPHsQ

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.

1.302 × 10⁹³(94-digit number)

13028702935377847592…79800232153708397279

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

1.302 × 10⁹³(94-digit number)

13028702935377847592…79800232153708397279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.605 × 10⁹³(94-digit number)

26057405870755695185…59600464307416794559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.211 × 10⁹³(94-digit number)

52114811741511390371…19200928614833589119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.042 × 10⁹⁴(95-digit number)

10422962348302278074…38401857229667178239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.084 × 10⁹⁴(95-digit number)

20845924696604556148…76803714459334356479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.169 × 10⁹⁴(95-digit number)

41691849393209112296…53607428918668712959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.338 × 10⁹⁴(95-digit number)

83383698786418224593…07214857837337425919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.667 × 10⁹⁵(96-digit number)

16676739757283644918…14429715674674851839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.335 × 10⁹⁵(96-digit number)

33353479514567289837…28859431349349703679

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