Block #274,515

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/26/2013, 7:57:54 AM · Difficulty 9.9577 · 6,543,454 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6485eec964f434a66a0c5bff3b9bbde4a314c87a1b61fb70f6b9dccf859e3b0b

View on Chainz ↗

Height

#274,515

Difficulty

9.957734

Transactions

Size

427 B

Version

Bits

09f52e08

Nonce

717

Timestamp

11/26/2013, 7:57:54 AM

Confirmations

6,543,454

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

51db5770f6607d8714829bc0b25d6eb9bef7921f5eb404926bc54561517b6759

Transactions (2)

Coinbase7231b3a855173a…0506a2ce079cab

1 in → 2 out10.0851 XPM141 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

f43ede2835d202…0ae8f4481fc297

1 in → 1 out0.3200 XPM192 B

AX3gi1Mo…4v25skFX

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.

2.040 × 10¹⁰³(104-digit number)

20405510363352918574…82576687899977767039

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

2.040 × 10¹⁰³(104-digit number)

20405510363352918574…82576687899977767039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.081 × 10¹⁰³(104-digit number)

40811020726705837148…65153375799955534079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.162 × 10¹⁰³(104-digit number)

81622041453411674296…30306751599911068159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.632 × 10¹⁰⁴(105-digit number)

16324408290682334859…60613503199822136319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.264 × 10¹⁰⁴(105-digit number)

32648816581364669718…21227006399644272639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.529 × 10¹⁰⁴(105-digit number)

65297633162729339436…42454012799288545279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.305 × 10¹⁰⁵(106-digit number)

13059526632545867887…84908025598577090559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.611 × 10¹⁰⁵(106-digit number)

26119053265091735774…69816051197154181119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.223 × 10¹⁰⁵(106-digit number)

52238106530183471549…39632102394308362239

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 #274,515

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