Block #81,038

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/24/2013, 12:17:00 PM · Difficulty 9.2647 · 6,745,903 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c6258a0aa78feb0e76cd1ec5511c119f5bed8bf4a64ae9872c47e5e80fbb5647

View on Chainz ↗

Height

#81,038

Difficulty

9.264708

Transactions

Size

699 B

Version

Bits

0943c3df

Nonce

291,524

Timestamp

7/24/2013, 12:17:00 PM

Confirmations

6,745,903

Mined by

⛏️ P2SHAKURVRyMJQuGsTAyTPovcYbdiciY4DGtd5

Merkle Root

ff5d2f0500e657f44c7982f306ffa5a252d978dc10d57471932cb954d6c0b5f7

Transactions (3)

Coinbase8a4a8fdd1cf937…1991652bf222cd

1 in → 1 out11.6500 XPM109 B

AKURVRyM…iY4DGtd5

c38e2ea733db79…af5b55aff7da58

1 in → 1 out11.7900 XPM158 B

AbhWjNtr…ZGT63E3Y

32e00eb7ce8107…7289e0c53e547e

2 in → 2 out12.5167 XPM340 B

AQXtZDNX…9LUNnhRc AQRpQZFN…ebNC2YCr

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.

1.489 × 10¹⁰⁰(101-digit number)

14892509749002950203…31761199625658382191

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

1.489 × 10¹⁰⁰(101-digit number)

14892509749002950203…31761199625658382191

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.978 × 10¹⁰⁰(101-digit number)

29785019498005900407…63522399251316764381

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.957 × 10¹⁰⁰(101-digit number)

59570038996011800815…27044798502633528761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.191 × 10¹⁰¹(102-digit number)

11914007799202360163…54089597005267057521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.382 × 10¹⁰¹(102-digit number)

23828015598404720326…08179194010534115041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.765 × 10¹⁰¹(102-digit number)

47656031196809440652…16358388021068230081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

9.531 × 10¹⁰¹(102-digit number)

95312062393618881305…32716776042136460161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.906 × 10¹⁰²(103-digit number)

19062412478723776261…65433552084272920321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.812 × 10¹⁰²(103-digit number)

38124824957447552522…30867104168545840641

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 #81,038

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