Block #271,103

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/24/2013, 10:29:24 AM · Difficulty 9.9515 · 6,536,084 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

1b7de98cb4afeab1965465a637c04232a9e4779738319e94248e7c2c16b70ecf

View on Chainz ↗

Height

#271,103

Difficulty

9.951466

Transactions

Size

832 B

Version

Bits

09f39347

Nonce

190,159

Timestamp

11/24/2013, 10:29:24 AM

Confirmations

6,536,084

Mined by

⛏️ "aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

48b790451cdb230452c7c0a354f7ebd8827c546d9cc3e552b96753daebbcb139

Transactions (1)

Coinbase48b790451cdb23…6753daebbcb139

1 in → 20 out10.0800 XPM743 B

APeshfYV…3PKcKMKH APVGazMT…cDCk2nwA ANQKf2g4…29NaVj23 ALdHh27b…XNbqrvPf 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.

1.934 × 10⁹¹(92-digit number)

19345894902528257762…63281833465837158399

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

1.934 × 10⁹¹(92-digit number)

19345894902528257762…63281833465837158399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.869 × 10⁹¹(92-digit number)

38691789805056515525…26563666931674316799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

7.738 × 10⁹¹(92-digit number)

77383579610113031050…53127333863348633599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.547 × 10⁹²(93-digit number)

15476715922022606210…06254667726697267199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.095 × 10⁹²(93-digit number)

30953431844045212420…12509335453394534399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.190 × 10⁹²(93-digit number)

61906863688090424840…25018670906789068799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.238 × 10⁹³(94-digit number)

12381372737618084968…50037341813578137599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.476 × 10⁹³(94-digit number)

24762745475236169936…00074683627156275199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.952 × 10⁹³(94-digit number)

49525490950472339872…00149367254312550399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

9.905 × 10⁹³(94-digit number)

99050981900944679745…00298734508625100799

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 #271,103

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