Block #313,766

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 12/15/2013, 3:21:26 PM · Difficulty 10.0255 · 6,480,503 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cd5c2638a2f141a4b175353a9fd50647313e1dc03d290c08585bd83859161497

View on Chainz ↗

Height

#313,766

Difficulty

10.025470

Transactions

Size

1006 B

Version

Bits

0a068536

Nonce

213,502

Timestamp

12/15/2013, 3:21:26 PM

Confirmations

6,480,503

Merkle Root

c9902db26779dcb659792b3fb142c5dff7befc7dd07a4cbbd05605a5b44c9cd7

Transactions (1)

Coinbasec9902db26779dc…5605a5b44c9cd7

1 in → 25 out9.9300 XPM913 B

AYtDvcGs…VuAcA7m7 AbtgNzNb…9Atvu81w Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe ASWX42VM…XypQABkY

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.

8.415 × 10¹⁰¹(102-digit number)

84157055846426181168…14997503613899848279

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

8.415 × 10¹⁰¹(102-digit number)

84157055846426181168…14997503613899848279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.683 × 10¹⁰²(103-digit number)

16831411169285236233…29995007227799696559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.366 × 10¹⁰²(103-digit number)

33662822338570472467…59990014455599393119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.732 × 10¹⁰²(103-digit number)

67325644677140944934…19980028911198786239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.346 × 10¹⁰³(104-digit number)

13465128935428188986…39960057822397572479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.693 × 10¹⁰³(104-digit number)

26930257870856377973…79920115644795144959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.386 × 10¹⁰³(104-digit number)

53860515741712755947…59840231289590289919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.077 × 10¹⁰⁴(105-digit number)

10772103148342551189…19680462579180579839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.154 × 10¹⁰⁴(105-digit number)

21544206296685102379…39360925158361159679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.308 × 10¹⁰⁴(105-digit number)

43088412593370204758…78721850316722319359

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