Block #138,715

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/28/2013, 1:46:32 PM · Difficulty 9.8280 · 6,660,203 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ff7bb6b5a5fd665a080ba6b9bfe15c0834c301076a2d92b114708d3f529994e8

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Height

#138,715

Difficulty

9.828047

Transactions

Size

1.14 KB

Version

Bits

09d3fadf

Nonce

47,331

Timestamp

8/28/2013, 1:46:32 PM

Confirmations

6,660,203

Mined by

⛏️ P2SHAZjdLUBVnhaTXpiom6JRDBkHMEpCUJqxcE

Merkle Root

501eb86d7afc6b0507e8a4a7ae81763ebb93a109a0e536b4a490926d569ac081

Transactions (2)

Coinbasec00c3be07539fd…4857a3050f12f1

1 in → 1 out10.3500 XPM109 B

AZjdLUBV…pCUJqxcE

ae4d4b34d51374…128c19dd6bc475

6 in → 2 out499.9170 XPM967 B

AUeFimzF…op75Mh53 AaaHGYrH…VQ7BtFyb

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.

2.549 × 10⁹⁴(95-digit number)

25491481330527421917…00678181988815083361

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

2.549 × 10⁹⁴(95-digit number)

25491481330527421917…00678181988815083361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.098 × 10⁹⁴(95-digit number)

50982962661054843835…01356363977630166721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.019 × 10⁹⁵(96-digit number)

10196592532210968767…02712727955260333441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.039 × 10⁹⁵(96-digit number)

20393185064421937534…05425455910520666881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.078 × 10⁹⁵(96-digit number)

40786370128843875068…10850911821041333761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.157 × 10⁹⁵(96-digit number)

81572740257687750136…21701823642082667521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.631 × 10⁹⁶(97-digit number)

16314548051537550027…43403647284165335041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.262 × 10⁹⁶(97-digit number)

32629096103075100054…86807294568330670081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.525 × 10⁹⁶(97-digit number)

65258192206150200109…73614589136661340161

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