Block #1,225,977

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/7/2015, 12:56:24 PM · Difficulty 10.7368 · 5,616,592 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

8b1b1930e4e26465303459809c7d9ee4bf0e8ef994c3e77a1b7d753eba09572b

View on Chainz ↗

Height

#1,225,977

Difficulty

10.736830

Transactions

Size

243 B

Version

Bits

0abca0de

Nonce

715,015,815

Timestamp

9/7/2015, 12:56:24 PM

Confirmations

5,616,592

Mined by

⛏️ P2SHAJJFkYGdzsqLDACHD3HDyenwiMUjCk4sEs

Merkle Root

b8b4e4dba1f1fda6af7e4b318b8dc3d078ae04996ae79518ba39050b619e2cbb

Transactions (1)

Coinbaseb8b4e4dba1f1fd…39050b619e2cbb

1 in → 2 out8.6600 XPM152 B

AJJFkYGd…UjCk4sEs ALPu3s2c…EJXLjVFh

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.

1.249 × 10⁹⁸(99-digit number)

12497870157862069644…54620892415659868159

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

1.249 × 10⁹⁸(99-digit number)

12497870157862069644…54620892415659868159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.499 × 10⁹⁸(99-digit number)

24995740315724139288…09241784831319736319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.999 × 10⁹⁸(99-digit number)

49991480631448278576…18483569662639472639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.998 × 10⁹⁸(99-digit number)

99982961262896557152…36967139325278945279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.999 × 10⁹⁹(100-digit number)

19996592252579311430…73934278650557890559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.999 × 10⁹⁹(100-digit number)

39993184505158622861…47868557301115781119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.998 × 10⁹⁹(100-digit number)

79986369010317245722…95737114602231562239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.599 × 10¹⁰⁰(101-digit number)

15997273802063449144…91474229204463124479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.199 × 10¹⁰⁰(101-digit number)

31994547604126898288…82948458408926248959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.398 × 10¹⁰⁰(101-digit number)

63989095208253796577…65896916817852497919

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

Block #1,225,977

Cookie Preferences