Block #159,033

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/10/2013, 8:11:19 PM · Difficulty 9.8656 · 6,632,879 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

46e52c59ff6aabc99f7f17543e9d05e4c864e0c7d3bac29f5a0066b0744697b3

View on Chainz ↗

Height

#159,033

Difficulty

9.865590

Transactions

Size

199 B

Version

Bits

09dd9753

Nonce

48,148

Timestamp

9/10/2013, 8:11:19 PM

Confirmations

6,632,879

Merkle Root

fe07e7d2f52ccae69dd0b2d8a0c3aea07a0ad0d724c1bb2072f4e3c722c47df6

Transactions (1)

Coinbasefe07e7d2f52cca…f4e3c722c47df6

1 in → 1 out10.2600 XPM109 B

AKhaGKFX…KjeAXtBv

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.

1.119 × 10⁹⁴(95-digit number)

11198474867236641841…22999611994670817119

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

1.119 × 10⁹⁴(95-digit number)

11198474867236641841…22999611994670817119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.239 × 10⁹⁴(95-digit number)

22396949734473283683…45999223989341634239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.479 × 10⁹⁴(95-digit number)

44793899468946567366…91998447978683268479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.958 × 10⁹⁴(95-digit number)

89587798937893134733…83996895957366536959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.791 × 10⁹⁵(96-digit number)

17917559787578626946…67993791914733073919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.583 × 10⁹⁵(96-digit number)

35835119575157253893…35987583829466147839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.167 × 10⁹⁵(96-digit number)

71670239150314507786…71975167658932295679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.433 × 10⁹⁶(97-digit number)

14334047830062901557…43950335317864591359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.866 × 10⁹⁶(97-digit number)

28668095660125803114…87900670635729182719

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