Block #150,347

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/4/2013, 11:17:28 PM · Difficulty 9.8590 · 6,642,203 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

51a0c904524414c97899491074eb235594dfe44970fec133ecc0bb2b11d5742d

View on Chainz ↗

Height

#150,347

Difficulty

9.858987

Transactions

Size

199 B

Version

Bits

09dbe696

Nonce

291,240

Timestamp

9/4/2013, 11:17:28 PM

Confirmations

6,642,203

Merkle Root

c48f16fa0942954512bf95def491e41f463eb5247ff72a85801a3526118cbe21

Transactions (1)

Coinbasec48f16fa094295…1a3526118cbe21

1 in → 1 out10.2700 XPM109 B

ATpY3yjG…xZyYqhas

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.

4.097 × 10⁹³(94-digit number)

40979972545047835937…01532745938173983839

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

4.097 × 10⁹³(94-digit number)

40979972545047835937…01532745938173983839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.195 × 10⁹³(94-digit number)

81959945090095671874…03065491876347967679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.639 × 10⁹⁴(95-digit number)

16391989018019134374…06130983752695935359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.278 × 10⁹⁴(95-digit number)

32783978036038268749…12261967505391870719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.556 × 10⁹⁴(95-digit number)

65567956072076537499…24523935010783741439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.311 × 10⁹⁵(96-digit number)

13113591214415307499…49047870021567482879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.622 × 10⁹⁵(96-digit number)

26227182428830614999…98095740043134965759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.245 × 10⁹⁵(96-digit number)

52454364857661229999…96191480086269931519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.049 × 10⁹⁶(97-digit number)

10490872971532245999…92382960172539863039

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