Block #80,897

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/24/2013, 10:21:01 AM · Difficulty 9.2608 · 6,708,657 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

cc048a7a52f9021bc36bdde7f134a91ffb74bd39dfe3a7ec83cc6da91c8430d0

View on Chainz ↗

Height

#80,897

Difficulty

9.260792

Transactions

Size

1.01 KB

Version

Bits

0942c33d

Nonce

76,678

Timestamp

7/24/2013, 10:21:01 AM

Confirmations

6,708,657

Merkle Root

6c959592b6dc468d387cdcd37c517c3e31453bd4026b6020e543568c6c2ad92c

Transactions (3)

Coinbasef63afe3cf3fbf5…66fe01492a6811

1 in → 1 out11.6600 XPM109 B

AcMDpWRb…vDUTfEYA

2af22826d4aa6e…8f2c6fc7c89ba3

4 in → 2 out330.7099 XPM670 B

AW3oqdog…1qjNKMmh ARvKwgZw…enrRDQGy

b17a67d579e69a…a1d88dac0ef09d

1 in → 1 out11.8900 XPM158 B

AHXsvpd1…2Hz7ryx6

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.

1.034 × 10¹⁰⁶(107-digit number)

10343582472412676336…90457589919999231959

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

1.034 × 10¹⁰⁶(107-digit number)

10343582472412676336…90457589919999231959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.068 × 10¹⁰⁶(107-digit number)

20687164944825352672…80915179839998463919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.137 × 10¹⁰⁶(107-digit number)

41374329889650705344…61830359679996927839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.274 × 10¹⁰⁶(107-digit number)

82748659779301410689…23660719359993855679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.654 × 10¹⁰⁷(108-digit number)

16549731955860282137…47321438719987711359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.309 × 10¹⁰⁷(108-digit number)

33099463911720564275…94642877439975422719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

6.619 × 10¹⁰⁷(108-digit number)

66198927823441128551…89285754879950845439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.323 × 10¹⁰⁸(109-digit number)

13239785564688225710…78571509759901690879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.647 × 10¹⁰⁸(109-digit number)

26479571129376451420…57143019519803381759

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