Block #212,776

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/16/2013, 12:23:29 PM · Difficulty 9.9193 · 6,597,950 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

fb2fa65568bf102318999ed33409c29616e16f41618d24cc0472913486f7d558

View on Chainz ↗

Height

#212,776

Difficulty

9.919322

Transactions

Size

202 B

Version

Bits

09eb58ab

Nonce

100,399

Timestamp

10/16/2013, 12:23:29 PM

Confirmations

6,597,950

Mined by

⛏️ P2SHATK4r8GhoVczEZqtspX4UTeEK5Usic4A9N

Merkle Root

a076177b3262d01f23eeac5c5055f081f006987faacba5ef071b4bd1d74e7f03

Transactions (1)

Coinbasea076177b3262d0…1b4bd1d74e7f03

1 in → 1 out10.1500 XPM109 B

ATK4r8Gh…Usic4A9N

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.

3.823 × 10¹⁰¹(102-digit number)

38237728771132238070…49884182999461892999

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

3.823 × 10¹⁰¹(102-digit number)

38237728771132238070…49884182999461892999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.647 × 10¹⁰¹(102-digit number)

76475457542264476140…99768365998923785999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.529 × 10¹⁰²(103-digit number)

15295091508452895228…99536731997847571999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.059 × 10¹⁰²(103-digit number)

30590183016905790456…99073463995695143999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.118 × 10¹⁰²(103-digit number)

61180366033811580912…98146927991390287999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.223 × 10¹⁰³(104-digit number)

12236073206762316182…96293855982780575999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.447 × 10¹⁰³(104-digit number)

24472146413524632364…92587711965561151999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.894 × 10¹⁰³(104-digit number)

48944292827049264729…85175423931122303999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.788 × 10¹⁰³(104-digit number)

97888585654098529459…70350847862244607999

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

Block #212,776

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