Block #147,201

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/2/2013, 11:06:50 PM · Difficulty 9.8514 · 6,662,346 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

570cebfed44bdbba29e3dfca52d5bcab9d5644939d8d112b91fccfc7ffb62c84

View on Chainz ↗

Height

#147,201

Difficulty

9.851379

Transactions

Size

198 B

Version

Bits

09d9f400

Nonce

176,888

Timestamp

9/2/2013, 11:06:50 PM

Confirmations

6,662,346

Mined by

⛏️ P2SHAa6PpN3XWen9U28VLp3hDw33d6XAm9RHxt

Merkle Root

05162b5b7e6284ce51c5e0a6cb2b786debe9f3564dbdc0e151606c06094ddde1

Transactions (1)

Coinbase05162b5b7e6284…606c06094ddde1

1 in → 1 out10.2900 XPM109 B

Aa6PpN3X…XAm9RHxt

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.

8.251 × 10⁹¹(92-digit number)

82516832942594507866…58839322484332293129

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

8.251 × 10⁹¹(92-digit number)

82516832942594507866…58839322484332293129

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.650 × 10⁹²(93-digit number)

16503366588518901573…17678644968664586259

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.300 × 10⁹²(93-digit number)

33006733177037803146…35357289937329172519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.601 × 10⁹²(93-digit number)

66013466354075606293…70714579874658345039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.320 × 10⁹³(94-digit number)

13202693270815121258…41429159749316690079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.640 × 10⁹³(94-digit number)

26405386541630242517…82858319498633380159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.281 × 10⁹³(94-digit number)

52810773083260485034…65716638997266760319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.056 × 10⁹⁴(95-digit number)

10562154616652097006…31433277994533520639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.112 × 10⁹⁴(95-digit number)

21124309233304194013…62866555989067041279

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 #147,201

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