Block #87,150

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 4:25:43 PM · Difficulty 9.2799 · 6,707,768 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d36c47d443d6f087311e72950ba85276df90267e72a1c2c06a40f21b4686c501

View on Chainz ↗

Height

#87,150

Difficulty

9.279904

Transactions

Size

206 B

Version

Bits

0947a7cd

Nonce

295,817

Timestamp

7/28/2013, 4:25:43 PM

Confirmations

6,707,768

Mined by

⛏️ P2SHATe7tG7XMJeCcfKBVw1awGupC6yczDSDEp

Merkle Root

a62a558714123756d289c7132b7a1a863a675868d106530a81f3a780fac019d4

Transactions (1)

Coinbasea62a5587141237…f3a780fac019d4

1 in → 1 out11.6000 XPM109 B

ATe7tG7X…yczDSDEp

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.

1.641 × 10¹¹¹(112-digit number)

16411576505621790694…51377860091457663799

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

1.641 × 10¹¹¹(112-digit number)

16411576505621790694…51377860091457663799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.282 × 10¹¹¹(112-digit number)

32823153011243581389…02755720182915327599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.564 × 10¹¹¹(112-digit number)

65646306022487162778…05511440365830655199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.312 × 10¹¹²(113-digit number)

13129261204497432555…11022880731661310399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.625 × 10¹¹²(113-digit number)

26258522408994865111…22045761463322620799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.251 × 10¹¹²(113-digit number)

52517044817989730222…44091522926645241599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.050 × 10¹¹³(114-digit number)

10503408963597946044…88183045853290483199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.100 × 10¹¹³(114-digit number)

21006817927195892089…76366091706580966399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.201 × 10¹¹³(114-digit number)

42013635854391784178…52732183413161932799

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