Block #60,869

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 10:16:41 AM · Difficulty 8.9710 · 6,750,058 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
59accc8a055c18d2919efc95821a918d620ccc07224cb2c0fa9e97e975dbe2f3

Height

#60,869

Difficulty

8.970996

Transactions

3

Size

1.36 KB

Version

2

Bits

08f89335

Nonce

303

Timestamp

7/18/2013, 10:16:41 AM

Confirmations

6,750,058

Merkle Root

c29bd9bf67c7bffedd6fc6c30203cb1bdb33ca7bf8f5cfce80bf7f25f2d1e8f0
Transactions (3)
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.

5.787 × 10¹⁰³(104-digit number)
57872314616265670248…47445669115649661121
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
5.787 × 10¹⁰³(104-digit number)
57872314616265670248…47445669115649661121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.157 × 10¹⁰⁴(105-digit number)
11574462923253134049…94891338231299322241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.314 × 10¹⁰⁴(105-digit number)
23148925846506268099…89782676462598644481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.629 × 10¹⁰⁴(105-digit number)
46297851693012536198…79565352925197288961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.259 × 10¹⁰⁴(105-digit number)
92595703386025072397…59130705850394577921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.851 × 10¹⁰⁵(106-digit number)
18519140677205014479…18261411700789155841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.703 × 10¹⁰⁵(106-digit number)
37038281354410028958…36522823401578311681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.407 × 10¹⁰⁵(106-digit number)
74076562708820057917…73045646803156623361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.481 × 10¹⁰⁶(107-digit number)
14815312541764011583…46091293606313246721
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:57,731,519 XPM·at block #6,810,926 · 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