Block #293,486

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 12/4/2013, 8:22:39 AM · Difficulty 9.9907 · 6,516,150 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e35f78c83d42e40892fe656cce4cfdb360499aa9981bf10cd7e466af6358be34

View on Chainz ↗

Height

#293,486

Difficulty

9.990659

Transactions

Size

1.11 KB

Version

Bits

09fd9bd7

Nonce

5,801

Timestamp

12/4/2013, 8:22:39 AM

Confirmations

6,516,150

Mined by

⛏️ nzaRAAWCkoGXK5wENDNCyHqfE3zcYk6zjpfLbCF

Merkle Root

b83731c6e974e3a16134acd90aa6c88d4e1605176aaab81de7bfa839b25a92a6

Transactions (1)

Coinbaseb83731c6e974e3…bfa839b25a92a6

1 in → 29 out9.9800 XPM1.02 KB

AWCkoGXK…zjpfLbCF AHVC5gC4…ymKvzTy7 AZDQWZv7…hXNTwZLR AaPASCNm…8mfBVejh AL5TiRPC…N8ZPmfzd

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.

1.188 × 10⁹²(93-digit number)

11883324311940141031…94926653772356694719

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

1.188 × 10⁹²(93-digit number)

11883324311940141031…94926653772356694719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.376 × 10⁹²(93-digit number)

23766648623880282062…89853307544713389439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.753 × 10⁹²(93-digit number)

47533297247760564124…79706615089426778879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.506 × 10⁹²(93-digit number)

95066594495521128248…59413230178853557759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.901 × 10⁹³(94-digit number)

19013318899104225649…18826460357707115519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.802 × 10⁹³(94-digit number)

38026637798208451299…37652920715414231039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.605 × 10⁹³(94-digit number)

76053275596416902598…75305841430828462079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.521 × 10⁹⁴(95-digit number)

15210655119283380519…50611682861656924159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.042 × 10⁹⁴(95-digit number)

30421310238566761039…01223365723313848319

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 #293,486

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