Block #68,709

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/20/2013, 5:22:13 AM · Difficulty 8.9899 · 6,727,291 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9e38948d959c7d2d15d963e168bc46a84161054de4b70a7958ef16dd8056c4b3

View on Chainz ↗

Height

#68,709

Difficulty

8.989912

Transactions

Size

1.79 KB

Version

Bits

08fd6ae2

Nonce

1,231

Timestamp

7/20/2013, 5:22:13 AM

Confirmations

6,727,291

Mined by

⛏️ P2SHAdiPqnNUbkj5hXLpHi5iuCLpu91T15f3GU

Merkle Root

8fddd35f97e043f1ee322db7ae15b00eb490b028825322bb98f342b7f7cbf683

Transactions (2)

Coinbase6b1f0bada4b9c7…abe56beac0169d

1 in → 1 out12.3800 XPM110 B

AdiPqnNU…1T15f3GU

26f6a16caefe93…86de34887dc9d3

14 in → 1 out250.0000 XPM1.60 KB

AQhTkauJ…uXtadFPR

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.

1.900 × 10⁹³(94-digit number)

19000110093486415230…03673358044488094959

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

1.900 × 10⁹³(94-digit number)

19000110093486415230…03673358044488094959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.800 × 10⁹³(94-digit number)

38000220186972830460…07346716088976189919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.600 × 10⁹³(94-digit number)

76000440373945660921…14693432177952379839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.520 × 10⁹⁴(95-digit number)

15200088074789132184…29386864355904759679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.040 × 10⁹⁴(95-digit number)

30400176149578264368…58773728711809519359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.080 × 10⁹⁴(95-digit number)

60800352299156528736…17547457423619038719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.216 × 10⁹⁵(96-digit number)

12160070459831305747…35094914847238077439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.432 × 10⁹⁵(96-digit number)

24320140919662611494…70189829694476154879

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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 8

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