Block #155,182

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/8/2013, 4:01:59 AM · Difficulty 9.8654 · 6,637,396 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5e268cbea781e3c1b815b8209e82cd24be71553bbca22e435ef49cb212d27dde

View on Chainz ↗

Height

#155,182

Difficulty

9.865415

Transactions

Size

198 B

Version

Bits

09dd8bd2

Nonce

73,086

Timestamp

9/8/2013, 4:01:59 AM

Confirmations

6,637,396

Merkle Root

d087ebc445ca8514d61d1c753bdc89ec82cd9663786b86cab5d909ef4fab2b31

Transactions (1)

Coinbased087ebc445ca85…d909ef4fab2b31

1 in → 1 out10.2600 XPM109 B

AP91QEDQ…W6JZAB9n

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.

2.596 × 10⁹²(93-digit number)

25960741895787294183…48961174423596584639

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

2.596 × 10⁹²(93-digit number)

25960741895787294183…48961174423596584639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.192 × 10⁹²(93-digit number)

51921483791574588366…97922348847193169279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.038 × 10⁹³(94-digit number)

10384296758314917673…95844697694386338559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.076 × 10⁹³(94-digit number)

20768593516629835346…91689395388772677119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.153 × 10⁹³(94-digit number)

41537187033259670693…83378790777545354239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.307 × 10⁹³(94-digit number)

83074374066519341386…66757581555090708479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.661 × 10⁹⁴(95-digit number)

16614874813303868277…33515163110181416959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.322 × 10⁹⁴(95-digit number)

33229749626607736554…67030326220362833919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.645 × 10⁹⁴(95-digit number)

66459499253215473108…34060652440725667839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.329 × 10⁹⁵(96-digit number)

13291899850643094621…68121304881451335679

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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