Block #60,008

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 5:31:05 AM · Difficulty 8.9674 · 6,736,893 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bb5c719bceda01b1c4c083d9f301e1174cbcb491cfd6adb87739009edb69c650

Height

#60,008

Difficulty

8.967425

Transactions

2

Size

360 B

Version

2

Bits

08f7a923

Nonce

516

Timestamp

7/18/2013, 5:31:05 AM

Confirmations

6,736,893

Merkle Root

d9f5750afdc0345262830a3f953bb857000ce800725bf5f64a818e51ffb629da
Transactions (2)
1 in → 1 out12.4300 XPM110 B
1 in → 1 out12.4700 XPM157 B
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.

2.256 × 10¹⁰¹(102-digit number)
22562478499243615033…91809822037227648401
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
2.256 × 10¹⁰¹(102-digit number)
22562478499243615033…91809822037227648401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.512 × 10¹⁰¹(102-digit number)
45124956998487230067…83619644074455296801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.024 × 10¹⁰¹(102-digit number)
90249913996974460135…67239288148910593601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.804 × 10¹⁰²(103-digit number)
18049982799394892027…34478576297821187201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.609 × 10¹⁰²(103-digit number)
36099965598789784054…68957152595642374401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.219 × 10¹⁰²(103-digit number)
72199931197579568108…37914305191284748801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.443 × 10¹⁰³(104-digit number)
14439986239515913621…75828610382569497601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.887 × 10¹⁰³(104-digit number)
28879972479031827243…51657220765138995201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.775 × 10¹⁰³(104-digit number)
57759944958063654486…03314441530277990401
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:57,619,228 XPM·at block #6,796,900 · updates every 60s
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