Block #300,239

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/8/2013, 11:48:32 AM · Difficulty 9.9922 · 6,497,912 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c3205b619cd01a3bd2d96459516b0104af589c9fec0fe19b31d5afff891fac99

View on Chainz ↗

Height

#300,239

Difficulty

9.992223

Transactions

Size

576 B

Version

Bits

09fe024e

Nonce

17,013

Timestamp

12/8/2013, 11:48:32 AM

Confirmations

6,497,912

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

195827a0008e6b57c91dcf053f7f6740dea98734e36161bb3adeaded10402f23

Transactions (2)

Coinbase24ea03700c5777…a3dd317c030133

1 in → 1 out10.0100 XPM110 B

AeKNrjNj…1NEq95Ta

9e3b2ee61d360e…681b1e103c3220

2 in → 2 out3.1132 XPM375 B

AH9zu7iW…Mt1CyZMe AYTrboja…JdbXeGRz

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.

2.002 × 10⁹⁶(97-digit number)

20026020837170186151…98235980385085913599

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

2.002 × 10⁹⁶(97-digit number)

20026020837170186151…98235980385085913599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.005 × 10⁹⁶(97-digit number)

40052041674340372303…96471960770171827199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.010 × 10⁹⁶(97-digit number)

80104083348680744606…92943921540343654399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.602 × 10⁹⁷(98-digit number)

16020816669736148921…85887843080687308799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.204 × 10⁹⁷(98-digit number)

32041633339472297842…71775686161374617599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.408 × 10⁹⁷(98-digit number)

64083266678944595685…43551372322749235199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.281 × 10⁹⁸(99-digit number)

12816653335788919137…87102744645498470399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.563 × 10⁹⁸(99-digit number)

25633306671577838274…74205489290996940799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.126 × 10⁹⁸(99-digit number)

51266613343155676548…48410978581993881599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.025 × 10⁹⁹(100-digit number)

10253322668631135309…96821957163987763199

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