Block #68,872

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/20/2013, 6:06:07 AM · Difficulty 8.9902 · 6,740,768 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

9d34059cac5da19639c17ab02fae992079442c8cffac1cd2e3aa838f17d3c9b8

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Height

#68,872

Difficulty

8.990153

Transactions

Size

362 B

Version

Bits

08fd7aa8

Nonce

Timestamp

7/20/2013, 6:06:07 AM

Confirmations

6,740,768

Mined by

⛏️ P2SHAYrtgdMxKPSUprai4iVmQwiyphSnFDNzsA

Merkle Root

caaed6dd849267693d389d19f0984724c6f98e20da3e75e8d42fcf13afa2d18a

Transactions (2)

Coinbasee8866c6df761de…f8c39b983274d4

1 in → 1 out12.3700 XPM110 B

AYrtgdMx…SnFDNzsA

ff9ca646723ce2…7a05bdf0c87268

1 in → 1 out12.4600 XPM158 B

AdSsHiaa…3ysMrPTh

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.

1.810 × 10¹⁰⁵(106-digit number)

18100399322754074412…68495646072188444171

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

1.810 × 10¹⁰⁵(106-digit number)

18100399322754074412…68495646072188444171

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.620 × 10¹⁰⁵(106-digit number)

36200798645508148825…36991292144376888341

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.240 × 10¹⁰⁵(106-digit number)

72401597291016297651…73982584288753776681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.448 × 10¹⁰⁶(107-digit number)

14480319458203259530…47965168577507553361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.896 × 10¹⁰⁶(107-digit number)

28960638916406519060…95930337155015106721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.792 × 10¹⁰⁶(107-digit number)

57921277832813038121…91860674310030213441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.158 × 10¹⁰⁷(108-digit number)

11584255566562607624…83721348620060426881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.316 × 10¹⁰⁷(108-digit number)

23168511133125215248…67442697240120853761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.633 × 10¹⁰⁷(108-digit number)

46337022266250430497…34885394480241707521

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

Block #68,872

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