Block #270,863

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/24/2013, 6:32:54 AM · Difficulty 9.9514 · 6,572,470 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

c735bee20458b286dec4576d981bcfe4db21d61e414f3cd42850ccae77fbee19

View on Chainz ↗

Height

#270,863

Difficulty

9.951437

Transactions

Size

1.98 KB

Version

Bits

09f39168

Nonce

212,795

Timestamp

11/24/2013, 6:32:54 AM

Confirmations

6,572,470

Mined by

⛏️ "aRATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

f3ac52db1d83ae1b66702805ac7c1553cd1fac6256c2e1ff9779c32a57a1e773

Transactions (1)

Coinbasef3ac52db1d83ae…79c32a57a1e773

1 in → 55 out10.0600 XPM1.89 KB

ATKK7iFz…wZm46KN1 ANmkKL2U…jPxj1Qs3 ARpndEmc…Hg792kEk AP2GxFDi…MZQBdSYt AexKjVEe…phmLMPem

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.

2.774 × 10⁹⁷(98-digit number)

27746104324618139091…37120764042093445119

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

2.774 × 10⁹⁷(98-digit number)

27746104324618139091…37120764042093445119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

5.549 × 10⁹⁷(98-digit number)

55492208649236278183…74241528084186890239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.109 × 10⁹⁸(99-digit number)

11098441729847255636…48483056168373780479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.219 × 10⁹⁸(99-digit number)

22196883459694511273…96966112336747560959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.439 × 10⁹⁸(99-digit number)

44393766919389022546…93932224673495121919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

8.878 × 10⁹⁸(99-digit number)

88787533838778045093…87864449346990243839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.775 × 10⁹⁹(100-digit number)

17757506767755609018…75728898693980487679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.551 × 10⁹⁹(100-digit number)

35515013535511218037…51457797387960975359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.103 × 10⁹⁹(100-digit number)

71030027071022436074…02915594775921950719

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 #270,863

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