Block #243,361

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/4/2013, 6:26:20 AM · Difficulty 9.9613 · 6,560,402 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

149817b85634f3b02c4dbef16d509e73ed48d6da357b54541c2d9b9e39d6b49e

View on Chainz ↗

Height

#243,361

Difficulty

9.961315

Transactions

Size

1.74 KB

Version

Bits

09f618c5

Nonce

20,147

Timestamp

11/4/2013, 6:26:20 AM

Confirmations

6,560,402

Mined by

⛏️ Rw>:AHxLfgpF3Ahonu63kdKbiGfoomaHZFyT2s

Merkle Root

cb60ca84c343d04eeb051fd2235513fb7658917f7258902e734740e51a621745

Transactions (1)

Coinbasecb60ca84c343d0…4740e51a621745

1 in → 48 out10.0400 XPM1.65 KB

AHxLfgpF…aHZFyT2s ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC AZWiC56x…NwextJca AKDTDDtx…iqvw9cdY

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.

6.047 × 10⁹⁴(95-digit number)

60470776415253507569…47677147053252019139

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

6.047 × 10⁹⁴(95-digit number)

60470776415253507569…47677147053252019139

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.209 × 10⁹⁵(96-digit number)

12094155283050701513…95354294106504038279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.418 × 10⁹⁵(96-digit number)

24188310566101403027…90708588213008076559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.837 × 10⁹⁵(96-digit number)

48376621132202806055…81417176426016153119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.675 × 10⁹⁵(96-digit number)

96753242264405612110…62834352852032306239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.935 × 10⁹⁶(97-digit number)

19350648452881122422…25668705704064612479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.870 × 10⁹⁶(97-digit number)

38701296905762244844…51337411408129224959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.740 × 10⁹⁶(97-digit number)

77402593811524489688…02674822816258449919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.548 × 10⁹⁷(98-digit number)

15480518762304897937…05349645632516899839

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