Block #86,969

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2013, 12:51:00 PM · Difficulty 9.2845 · 6,729,286 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

2ce7b5298902a64e04240479ba0466b1d0047aa94f0dba1c911d6072c7969afa

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Height

#86,969

Difficulty

9.284548

Transactions

Size

213 B

Version

Bits

0948d81e

Nonce

120,688

Timestamp

7/28/2013, 12:51:00 PM

Confirmations

6,729,286

Mined by

⛏️ P2SHAeEXQxqG1a9HUoHobjrNQ1M2oHJ2q5dxWc

Merkle Root

59da0879312c53c633a500daf0056935bdf7b731854bfcd209a042cb61082142

Transactions (1)

Coinbase59da0879312c53…a042cb61082142

1 in → 1 out11.5800 XPM109 B

AeEXQxqG…J2q5dxWc

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.

2.589 × 10¹²⁷(128-digit number)

25898612437826695129…14343662451744662179

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

2.589 × 10¹²⁷(128-digit number)

25898612437826695129…14343662451744662179

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.179 × 10¹²⁷(128-digit number)

51797224875653390258…28687324903489324359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.035 × 10¹²⁸(129-digit number)

10359444975130678051…57374649806978648719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.071 × 10¹²⁸(129-digit number)

20718889950261356103…14749299613957297439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.143 × 10¹²⁸(129-digit number)

41437779900522712207…29498599227914594879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.287 × 10¹²⁸(129-digit number)

82875559801045424414…58997198455829189759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.657 × 10¹²⁹(130-digit number)

16575111960209084882…17994396911658379519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.315 × 10¹²⁹(130-digit number)

33150223920418169765…35988793823316759039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.630 × 10¹²⁹(130-digit number)

66300447840836339531…71977587646633518079

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

Block #86,969

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