Block #167,204

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/16/2013, 10:36:11 AM · Difficulty 9.8688 · 6,628,859 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

9e3c7a1f27c1ecc71e523c2999391356abe8db1921e08e05912bc0fc84825cf6

View on Chainz ↗

Height

#167,204

Difficulty

9.868760

Transactions

Size

1.07 KB

Version

Bits

09de6711

Nonce

287,786

Timestamp

9/16/2013, 10:36:11 AM

Confirmations

6,628,859

Mined by

⛏️ P2SHAH9m5LJX9BqreMSnkqQ1dy6xMVEWCVuysW

Merkle Root

e22fcf6b5ad30e1d77eac6a451733c8db483bed4eb795888176d0ec51024b981

Transactions (3)

Coinbasedb44fb370c85fd…00d0ce6429f576

1 in → 1 out10.2700 XPM109 B

AH9m5LJX…EWCVuysW

52c63de41905ab…f88071ebb2e42e

2 in → 2 out0.1100 XPM373 B

Ae6wSxSy…tLzg98jk AcrGt9qf…MSqF3fwR

8e9392f7c13d26…cfd4452f6800a4

3 in → 2 out0.1128 XPM523 B

AHUsfavA…ejt9qyB1 AU61evFv…pm8c8Rhf

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.

7.301 × 10¹⁰³(104-digit number)

73017365738766478049…31698201794297594879

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

7.301 × 10¹⁰³(104-digit number)

73017365738766478049…31698201794297594879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.460 × 10¹⁰⁴(105-digit number)

14603473147753295609…63396403588595189759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.920 × 10¹⁰⁴(105-digit number)

29206946295506591219…26792807177190379519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

5.841 × 10¹⁰⁴(105-digit number)

58413892591013182439…53585614354380759039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.168 × 10¹⁰⁵(106-digit number)

11682778518202636487…07171228708761518079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.336 × 10¹⁰⁵(106-digit number)

23365557036405272975…14342457417523036159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

4.673 × 10¹⁰⁵(106-digit number)

46731114072810545951…28684914835046072319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

9.346 × 10¹⁰⁵(106-digit number)

93462228145621091902…57369829670092144639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.869 × 10¹⁰⁶(107-digit number)

18692445629124218380…14739659340184289279

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