Block #81,159

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/24/2013, 2:17:36 PM · Difficulty 9.2644 · 6,710,367 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a1060d491bbe50482afee3ad1b7917da49ca964340d6f897eb6337d16f7c65fc

View on Chainz ↗

Height

#81,159

Difficulty

9.264448

Transactions

Size

204 B

Version

Bits

0943b2e0

Nonce

75,153

Timestamp

7/24/2013, 2:17:36 PM

Confirmations

6,710,367

Merkle Root

cb0bb79495f1b9bfa7fff322283ff8bc2130f143b3a07192bb190dad3fa7e866

Transactions (1)

Coinbasecb0bb79495f1b9…190dad3fa7e866

1 in → 1 out11.6300 XPM109 B

AHGi8wDB…eKomrPdd

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.

8.347 × 10¹⁰⁶(107-digit number)

83478069222132276000…85142633731001319319

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

8.347 × 10¹⁰⁶(107-digit number)

83478069222132276000…85142633731001319319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.669 × 10¹⁰⁷(108-digit number)

16695613844426455200…70285267462002638639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.339 × 10¹⁰⁷(108-digit number)

33391227688852910400…40570534924005277279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.678 × 10¹⁰⁷(108-digit number)

66782455377705820800…81141069848010554559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.335 × 10¹⁰⁸(109-digit number)

13356491075541164160…62282139696021109119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.671 × 10¹⁰⁸(109-digit number)

26712982151082328320…24564279392042218239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.342 × 10¹⁰⁸(109-digit number)

53425964302164656640…49128558784084436479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.068 × 10¹⁰⁹(110-digit number)

10685192860432931328…98257117568168872959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.137 × 10¹⁰⁹(110-digit number)

21370385720865862656…96514235136337745919

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