Block #276,699

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/27/2013, 7:12:52 AM · Difficulty 9.9639 · 6,531,566 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

36a7d22b19e06e7fe8da47f17d43691f71983a207d3d79666c776a413370ef39

View on Chainz ↗

Height

#276,699

Difficulty

9.963921

Transactions

Size

1.11 KB

Version

Bits

09f6c38a

Nonce

62,357

Timestamp

11/27/2013, 7:12:52 AM

Confirmations

6,531,566

Mined by

⛏️ 8aR\APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

122f77ba4c196dce0ecbe20133301ec6f91ab4329b782961af5fd2c0de24aaf0

Transactions (1)

Coinbase122f77ba4c196d…5fd2c0de24aaf0

1 in → 29 out10.0400 XPM1.02 KB

APeshfYV…3PKcKMKH AScAzqGc…BZ6tV1vJ ANmkKL2U…jPxj1Qs3 AWXYBWKP…qQAoisBJ ATnPEc1T…ndE5zGvr

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.

2.502 × 10⁹⁵(96-digit number)

25026858175768181159…07063175856530341439

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

2.502 × 10⁹⁵(96-digit number)

25026858175768181159…07063175856530341439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.005 × 10⁹⁵(96-digit number)

50053716351536362319…14126351713060682879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.001 × 10⁹⁶(97-digit number)

10010743270307272463…28252703426121365759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.002 × 10⁹⁶(97-digit number)

20021486540614544927…56505406852242731519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.004 × 10⁹⁶(97-digit number)

40042973081229089855…13010813704485463039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.008 × 10⁹⁶(97-digit number)

80085946162458179710…26021627408970926079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.601 × 10⁹⁷(98-digit number)

16017189232491635942…52043254817941852159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.203 × 10⁹⁷(98-digit number)

32034378464983271884…04086509635883704319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.406 × 10⁹⁷(98-digit number)

64068756929966543768…08173019271767408639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.281 × 10⁹⁸(99-digit number)

12813751385993308753…16346038543534817279

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 #276,699

Cookie Preferences