Block #81,107

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/24/2013, 1:25:44 PM · Difficulty 9.2646 · 6,713,954 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6eecf5a48566814b3cab3483c0ddd9bec765f6d42d2eebac56cf59537943edd0

View on Chainz ↗

Height

#81,107

Difficulty

9.264599

Transactions

Size

588 B

Version

Bits

0943bcbb

Nonce

196,729

Timestamp

7/24/2013, 1:25:44 PM

Confirmations

6,713,954

Mined by

⛏️ P2SHAHGi8wDB5Q1pnktV2RKKJj33qeeKomrPdd

Merkle Root

75d419598d322d1c80d54003cea4775fd6d87e6760651814c1bad0dfb0207a41

Transactions (2)

Coinbasef85c891b6662f1…ced933368e18db

1 in → 1 out11.6400 XPM109 B

AHGi8wDB…eKomrPdd

c7d92c186bdb48…3485dd24f7ad0e

3 in → 1 out36.7500 XPM389 B

AbAsvJzY…WXE9KEcQ

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.

3.934 × 10⁹⁴(95-digit number)

39349210301199551881…02961760987458237359

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

3.934 × 10⁹⁴(95-digit number)

39349210301199551881…02961760987458237359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.869 × 10⁹⁴(95-digit number)

78698420602399103763…05923521974916474719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.573 × 10⁹⁵(96-digit number)

15739684120479820752…11847043949832949439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.147 × 10⁹⁵(96-digit number)

31479368240959641505…23694087899665898879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.295 × 10⁹⁵(96-digit number)

62958736481919283011…47388175799331797759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.259 × 10⁹⁶(97-digit number)

12591747296383856602…94776351598663595519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.518 × 10⁹⁶(97-digit number)

25183494592767713204…89552703197327191039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.036 × 10⁹⁶(97-digit number)

50366989185535426408…79105406394654382079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.007 × 10⁹⁷(98-digit number)

10073397837107085281…58210812789308764159

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