Block #270,709

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/24/2013, 3:50:56 AM · Difficulty 9.9515 · 6,570,047 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6b57962e09e0004c4ab98b3f1f065c5643b2e4a109f41000dd6e93a241b89540

View on Chainz ↗

Height

#270,709

Difficulty

9.951508

Transactions

Size

1.41 KB

Version

Bits

09f39607

Nonce

400

Timestamp

11/24/2013, 3:50:56 AM

Confirmations

6,570,047

Mined by

⛏️ u!aRw!ALK5HNZYPHizMT3nnsa8og2434KLLKfgMj

Merkle Root

372c6e32c9450b818b756cbad0be0ada639006b9f5d27b5cdecbea35ffc78abc

Transactions (1)

Coinbase372c6e32c9450b…cbea35ffc78abc

1 in → 38 out10.0600 XPM1.32 KB

ALK5HNZY…KLLKfgMj ATKK7iFz…wZm46KN1 APVGazMT…cDCk2nwA AJaGRnaj…iCHGoy6E AMbCuLHZ…WSoStwkc

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.

3.177 × 10¹⁰⁰(101-digit number)

31773410170871367450…87944720605355678719

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

3.177 × 10¹⁰⁰(101-digit number)

31773410170871367450…87944720605355678719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.354 × 10¹⁰⁰(101-digit number)

63546820341742734900…75889441210711357439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.270 × 10¹⁰¹(102-digit number)

12709364068348546980…51778882421422714879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.541 × 10¹⁰¹(102-digit number)

25418728136697093960…03557764842845429759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.083 × 10¹⁰¹(102-digit number)

50837456273394187920…07115529685690859519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.016 × 10¹⁰²(103-digit number)

10167491254678837584…14231059371381719039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.033 × 10¹⁰²(103-digit number)

20334982509357675168…28462118742763438079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.066 × 10¹⁰²(103-digit number)

40669965018715350336…56924237485526876159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.133 × 10¹⁰²(103-digit number)

81339930037430700672…13848474971053752319

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 #270,709

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