Block #163,306

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/13/2013, 9:56:22 PM · Difficulty 9.8617 · 6,644,313 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

59812f8dbf5525cb18105e15ef71e9c01a3fa6280bef517fe4b82717c87136e3

View on Chainz ↗

Height

#163,306

Difficulty

9.861749

Transactions

Size

720 B

Version

Bits

09dc9b99

Nonce

348,462

Timestamp

9/13/2013, 9:56:22 PM

Confirmations

6,644,313

Mined by

⛏️ P2SHAJQ1aTBySnuwnLtsc8mHdZcsu2oyXa68D5

Merkle Root

4bda301fb397e9ede727ca20ffd0d48d23195fad4669635f59d197503abf23a6

Transactions (2)

Coinbase0fc01c5d06a8ae…85dbc26910eeb2

1 in → 1 out10.2800 XPM109 B

AJQ1aTBy…oyXa68D5

06478204aeda8d…5a072146eab67e

3 in → 2 out150.0129 XPM522 B

AG6wxEar…NaiibHgf AXCoN6AA…zcf98WDF

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.

1.265 × 10⁹³(94-digit number)

12654578558321822143…66138973779769889281

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

1.265 × 10⁹³(94-digit number)

12654578558321822143…66138973779769889281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.530 × 10⁹³(94-digit number)

25309157116643644287…32277947559539778561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

5.061 × 10⁹³(94-digit number)

50618314233287288575…64555895119079557121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.012 × 10⁹⁴(95-digit number)

10123662846657457715…29111790238159114241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.024 × 10⁹⁴(95-digit number)

20247325693314915430…58223580476318228481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

4.049 × 10⁹⁴(95-digit number)

40494651386629830860…16447160952636456961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

8.098 × 10⁹⁴(95-digit number)

80989302773259661721…32894321905272913921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.619 × 10⁹⁵(96-digit number)

16197860554651932344…65788643810545827841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.239 × 10⁹⁵(96-digit number)

32395721109303864688…31577287621091655681

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 #163,306

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