Block #213,625

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/16/2013, 11:42:46 PM · Difficulty 9.9220 · 6,578,854 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

12c4467902aff56df1c4adde8b141482a042da867d089b1658348a101575b6ee

View on Chainz ↗

Height

#213,625

Difficulty

9.922037

Transactions

Size

1.18 KB

Version

Bits

09ec0aa0

Nonce

561,380

Timestamp

10/16/2013, 11:42:46 PM

Confirmations

6,578,854

Merkle Root

7d58246a7f1e560859ed7a06e0b887d8bf67bf593321c910c79642815ef1ac75

Transactions (3)

Coinbased46ba76d804df1…126561f5eba882

1 in → 1 out10.2500 XPM109 B

ASgfxRjp…cBStWjGx

9abb367f91b1f6…8513ca39f9ce88

3 in → 2 out257.9327 XPM521 B

AMRZRGe5…kYxt7p4F AKcwruc8…XhAGZ5iV

e4b527a912c69f…499ec90afbcb49

3 in → 4 out30.5700 XPM487 B

AdSKb2ue…gskipCSD AHLyZUb7…cHnQjZJ9 AQXUSoBL…CzbjKp8b AbuU1HhS…JPwsJEbB

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.

1.666 × 10⁹⁴(95-digit number)

16664088523058631319…34998273727146157199

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

1.666 × 10⁹⁴(95-digit number)

16664088523058631319…34998273727146157199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.332 × 10⁹⁴(95-digit number)

33328177046117262638…69996547454292314399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.665 × 10⁹⁴(95-digit number)

66656354092234525276…39993094908584628799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.333 × 10⁹⁵(96-digit number)

13331270818446905055…79986189817169257599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.666 × 10⁹⁵(96-digit number)

26662541636893810110…59972379634338515199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.332 × 10⁹⁵(96-digit number)

53325083273787620221…19944759268677030399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.066 × 10⁹⁶(97-digit number)

10665016654757524044…39889518537354060799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.133 × 10⁹⁶(97-digit number)

21330033309515048088…79779037074708121599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.266 × 10⁹⁶(97-digit number)

42660066619030096177…59558074149416243199

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