Block #248,615

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/7/2013, 12:02:02 PM · Difficulty 9.9659 · 6,568,414 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

d9c148afa963af959856c2acaeca24dd776bce5e32c0b51ef3966fae42dc9cf4

View on Chainz ↗

Height

#248,615

Difficulty

9.965863

Transactions

Size

1.78 KB

Version

Bits

09f742d0

Nonce

177,171

Timestamp

11/7/2013, 12:02:02 PM

Confirmations

6,568,414

Mined by

⛏️ 'R{AKXeSXzuNp3rXfbvqBPuAUeHUgyeuNjvhB

Merkle Root

98dce5358e618583f534ed5bc07f5988e807957ee8833e14c3426c0bd3d9d060

Transactions (1)

Coinbase98dce5358e6185…426c0bd3d9d060

1 in → 49 out10.0300 XPM1.69 KB

AKXeSXzu…yeuNjvhB ARpndEmc…Hg792kEk AKDTDDtx…iqvw9cdY AcoeyB14…sNGTo8wS AJzWx2VD…j4ZSMit5

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.

5.011 × 10⁹³(94-digit number)

50117400863092292108…62709594445956369019

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

5.011 × 10⁹³(94-digit number)

50117400863092292108…62709594445956369019

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.002 × 10⁹⁴(95-digit number)

10023480172618458421…25419188891912738039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.004 × 10⁹⁴(95-digit number)

20046960345236916843…50838377783825476079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.009 × 10⁹⁴(95-digit number)

40093920690473833686…01676755567650952159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.018 × 10⁹⁴(95-digit number)

80187841380947667373…03353511135301904319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.603 × 10⁹⁵(96-digit number)

16037568276189533474…06707022270603808639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.207 × 10⁹⁵(96-digit number)

32075136552379066949…13414044541207617279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.415 × 10⁹⁵(96-digit number)

64150273104758133899…26828089082415234559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.283 × 10⁹⁶(97-digit number)

12830054620951626779…53656178164830469119

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 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

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 1CC formula:

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

Cross-reference on Chainz Explorer

Block #248,615

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