Block #248,138

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/7/2013, 5:09:22 AM · Difficulty 9.9654 · 6,554,536 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4db2963d417ea8a13ca68981d9155afcb9d2b542c8f8e27816b8ea40a189bc83

View on Chainz ↗

Height

#248,138

Difficulty

9.965403

Transactions

Size

1.97 KB

Version

Bits

09f724a0

Nonce

324,593

Timestamp

11/7/2013, 5:09:22 AM

Confirmations

6,554,536

Mined by

⛏️ JR{AMdvB6BSeR5j7BaEUYaiSNxidBDPq9FYdA

Merkle Root

67ce1f3fc2491f8112d27e15c527191087adbc545eeabc7600e90b80e76dcdae

Transactions (1)

Coinbase67ce1f3fc2491f…e90b80e76dcdae

1 in → 55 out10.0300 XPM1.89 KB

AMdvB6BS…DPq9FYdA ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY ANo4YY1x…vnsPRDSU

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.

1.276 × 10⁹³(94-digit number)

12763215159665719351…09074283492934174719

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

1.276 × 10⁹³(94-digit number)

12763215159665719351…09074283492934174719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.552 × 10⁹³(94-digit number)

25526430319331438703…18148566985868349439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.105 × 10⁹³(94-digit number)

51052860638662877407…36297133971736698879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.021 × 10⁹⁴(95-digit number)

10210572127732575481…72594267943473397759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.042 × 10⁹⁴(95-digit number)

20421144255465150963…45188535886946795519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.084 × 10⁹⁴(95-digit number)

40842288510930301926…90377071773893591039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

8.168 × 10⁹⁴(95-digit number)

81684577021860603852…80754143547787182079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.633 × 10⁹⁵(96-digit number)

16336915404372120770…61508287095574364159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.267 × 10⁹⁵(96-digit number)

32673830808744241541…23016574191148728319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.534 × 10⁹⁵(96-digit number)

65347661617488483082…46033148382297456639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 1CC formula:

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

Cross-reference on Chainz Explorer