Block #48,838

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/15/2013, 5:16:45 PM · Difficulty 8.8533 · 6,742,813 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

59192aede612ec6fb1645984e5882d17e63f7037dcfd5d1128466f23cae84384

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Height

#48,838

Difficulty

8.853346

Transactions

Size

364 B

Version

Bits

08da74dc

Nonce

385

Timestamp

7/15/2013, 5:16:45 PM

Confirmations

6,742,813

Merkle Root

6b418171e695355f014d3c1b15adb4dcc0bf1711f1215cce21981b5ed62ee283

Transactions (2)

Coinbase64bdb9db1664dc…8b1dc955da6aee

1 in → 1 out12.7500 XPM110 B

AVB3XWmS…yrepFXCW

6e9ae8187ac863…b76a9a9cb84068

1 in → 1 out12.9900 XPM159 B

AG43TCYA…UW1AUz7e

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.

7.598 × 10¹⁰⁶(107-digit number)

75987333122753777357…15554414088951572161

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

7.598 × 10¹⁰⁶(107-digit number)

75987333122753777357…15554414088951572161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.519 × 10¹⁰⁷(108-digit number)

15197466624550755471…31108828177903144321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.039 × 10¹⁰⁷(108-digit number)

30394933249101510942…62217656355806288641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.078 × 10¹⁰⁷(108-digit number)

60789866498203021885…24435312711612577281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.215 × 10¹⁰⁸(109-digit number)

12157973299640604377…48870625423225154561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.431 × 10¹⁰⁸(109-digit number)

24315946599281208754…97741250846450309121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.863 × 10¹⁰⁸(109-digit number)

48631893198562417508…95482501692900618241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

9.726 × 10¹⁰⁸(109-digit number)

97263786397124835017…90965003385801236481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.945 × 10¹⁰⁹(110-digit number)

19452757279424967003…81930006771602472961

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