Block #60,074

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 5:58:17 AM · Difficulty 8.9677 · 6,747,025 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ffef918f3bbe4a259be9e275996d9bfc28accd00cd0e7ba0de2763777bfbffa

Height

#60,074

Difficulty

8.967677

Transactions

2

Size

871 B

Version

2

Bits

08f7b9ad

Nonce

240

Timestamp

7/18/2013, 5:58:17 AM

Confirmations

6,747,025

Merkle Root

78dda93562af77877e2a88709d65d2c1e14300cd3fa9a16ff11058b5eadaccbc
Transactions (2)
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.

8.817 × 10⁹⁶(97-digit number)
88171751135987602076…69336919644965032961
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.

1
origin + 1
8.817 × 10⁹⁶(97-digit number)
88171751135987602076…69336919644965032961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.763 × 10⁹⁷(98-digit number)
17634350227197520415…38673839289930065921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.526 × 10⁹⁷(98-digit number)
35268700454395040830…77347678579860131841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.053 × 10⁹⁷(98-digit number)
70537400908790081661…54695357159720263681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.410 × 10⁹⁸(99-digit number)
14107480181758016332…09390714319440527361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.821 × 10⁹⁸(99-digit number)
28214960363516032664…18781428638881054721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.642 × 10⁹⁸(99-digit number)
56429920727032065328…37562857277762109441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.128 × 10⁹⁹(100-digit number)
11285984145406413065…75125714555524218881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.257 × 10⁹⁹(100-digit number)
22571968290812826131…50251429111048437761
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,700,891 XPM·at block #6,807,098 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy