Block #83,253

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/26/2013, 12:38:48 AM · Difficulty 9.2694 · 6,707,690 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

377ba2f69130d1e768c3ecab5baffa5196cac2b9f3b2f7b94fc10b6f8104f514

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Height

#83,253

Difficulty

9.269351

Transactions

Size

874 B

Version

Bits

0944f437

Nonce

55,350

Timestamp

7/26/2013, 12:38:48 AM

Confirmations

6,707,690

Merkle Root

21e4093c6724d1607544474eaf6b4442f7ae368918e032e619f97fea7dd19f29

Transactions (2)

Coinbasef82ceb2e5358a8…dce81128b6992b

1 in → 1 out11.6300 XPM109 B

AcuJraLT…Y66BS47Q

2322c0e7369272…6fff8573cddea0

4 in → 2 out150.0135 XPM671 B

AXAdc5sP…JAVZqDWd AMXVaUL3…43tGXQHE

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.

5.210 × 10¹⁰³(104-digit number)

52109618490739843244…85354927170045825409

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

5.210 × 10¹⁰³(104-digit number)

52109618490739843244…85354927170045825409

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.042 × 10¹⁰⁴(105-digit number)

10421923698147968648…70709854340091650819

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.084 × 10¹⁰⁴(105-digit number)

20843847396295937297…41419708680183301639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.168 × 10¹⁰⁴(105-digit number)

41687694792591874595…82839417360366603279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.337 × 10¹⁰⁴(105-digit number)

83375389585183749191…65678834720733206559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.667 × 10¹⁰⁵(106-digit number)

16675077917036749838…31357669441466413119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.335 × 10¹⁰⁵(106-digit number)

33350155834073499676…62715338882932826239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

6.670 × 10¹⁰⁵(106-digit number)

66700311668146999352…25430677765865652479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.334 × 10¹⁰⁶(107-digit number)

13340062333629399870…50861355531731304959

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