Block #96,022

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/3/2013, 11:51:29 PM · Difficulty 9.2516 · 6,729,531 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

102f1fcbc8b136b0b20e43dc7b9e113d94df6e8197dad22837fa0ba0ab472680

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Height

#96,022

Difficulty

9.251616

Transactions

Size

203 B

Version

Bits

094069e8

Nonce

84,481

Timestamp

8/3/2013, 11:51:29 PM

Confirmations

6,729,531

Mined by

⛏️ P2SHAPfSKTmUn64oSBAFQniUR7xVYh7w2oQvEV

Merkle Root

c5b7566fbb95f186db85fc06f455f50b6b96f2369fe0c00debcbd3ad910863e5

Transactions (1)

Coinbasec5b7566fbb95f1…cbd3ad910863e5

1 in → 1 out11.6700 XPM109 B

APfSKTmU…7w2oQvEV

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.

3.276 × 10¹⁰⁵(106-digit number)

32765687735691441129…72507867758010389121

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

3.276 × 10¹⁰⁵(106-digit number)

32765687735691441129…72507867758010389121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.553 × 10¹⁰⁵(106-digit number)

65531375471382882259…45015735516020778241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.310 × 10¹⁰⁶(107-digit number)

13106275094276576451…90031471032041556481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.621 × 10¹⁰⁶(107-digit number)

26212550188553152903…80062942064083112961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.242 × 10¹⁰⁶(107-digit number)

52425100377106305807…60125884128166225921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.048 × 10¹⁰⁷(108-digit number)

10485020075421261161…20251768256332451841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.097 × 10¹⁰⁷(108-digit number)

20970040150842522323…40503536512664903681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.194 × 10¹⁰⁷(108-digit number)

41940080301685044646…81007073025329807361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.388 × 10¹⁰⁷(108-digit number)

83880160603370089292…62014146050659614721

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer

Block #96,022

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