Block #77,497

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/22/2013, 10:46:17 AM · Difficulty 9.1767 · 6,714,497 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

55951840f2098e39d9b6cdc790ede0bb9d04bb64c4bd47f71e53f493a959d4d9

View on Chainz ↗

Height

#77,497

Difficulty

9.176722

Transactions

Size

691 B

Version

Bits

092d3d9f

Nonce

572

Timestamp

7/22/2013, 10:46:17 AM

Confirmations

6,714,497

Merkle Root

7c9d64d154f0b0ccef17fda57e0fcb7f00c1539fb4c322e40e3ab8bd5d853228

Transactions (2)

Coinbaseb009f6003846dd…e91c2aca6922ae

1 in → 1 out11.8700 XPM110 B

AKvxfcss…SMGzmwyo

c301a8997c2f6d…6a1052236c02ac

3 in → 1 out273.6040 XPM489 B

ALWQvoi6…1ybUDaYR

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.

5.616 × 10⁹⁹(100-digit number)

56163217392335544479…90082821387112120559

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

5.616 × 10⁹⁹(100-digit number)

56163217392335544479…90082821387112120559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.123 × 10¹⁰⁰(101-digit number)

11232643478467108895…80165642774224241119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.246 × 10¹⁰⁰(101-digit number)

22465286956934217791…60331285548448482239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.493 × 10¹⁰⁰(101-digit number)

44930573913868435583…20662571096896964479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

8.986 × 10¹⁰⁰(101-digit number)

89861147827736871167…41325142193793928959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.797 × 10¹⁰¹(102-digit number)

17972229565547374233…82650284387587857919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.594 × 10¹⁰¹(102-digit number)

35944459131094748466…65300568775175715839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.188 × 10¹⁰¹(102-digit number)

71888918262189496933…30601137550351431679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.437 × 10¹⁰²(103-digit number)

14377783652437899386…61202275100702863359

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