Block #86,344

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 1:45:55 AM · Difficulty 9.2901 · 6,707,771 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9360bac41c1c830b0626178389dd34ea24dc9164c9b8fc91a511b67bc91f43d2

View on Chainz ↗

Height

#86,344

Difficulty

9.290132

Transactions

Size

205 B

Version

Bits

094a4610

Nonce

169,813

Timestamp

7/28/2013, 1:45:55 AM

Confirmations

6,707,771

Merkle Root

66a48f7ba495f9fe3857dce4a32e6f178e0f377e908a92ac42da3072f84eaf1c

Transactions (1)

Coinbase66a48f7ba495f9…da3072f84eaf1c

1 in → 1 out11.5700 XPM109 B

AcBadmkp…GmhL921o

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.

1.465 × 10¹⁰⁹(110-digit number)

14654084955680740594…49195780860236361939

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

1.465 × 10¹⁰⁹(110-digit number)

14654084955680740594…49195780860236361939

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.930 × 10¹⁰⁹(110-digit number)

29308169911361481189…98391561720472723879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.861 × 10¹⁰⁹(110-digit number)

58616339822722962379…96783123440945447759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.172 × 10¹¹⁰(111-digit number)

11723267964544592475…93566246881890895519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.344 × 10¹¹⁰(111-digit number)

23446535929089184951…87132493763781791039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.689 × 10¹¹⁰(111-digit number)

46893071858178369903…74264987527563582079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.378 × 10¹¹⁰(111-digit number)

93786143716356739806…48529975055127164159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.875 × 10¹¹¹(112-digit number)

18757228743271347961…97059950110254328319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.751 × 10¹¹¹(112-digit number)

37514457486542695922…94119900220508656639

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