Block #60,106

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/18/2013, 6:10:31 AM · Difficulty 8.9678 · 6,745,078 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
beda22ed5c125b53eb6376c87e66e8415f77d95cb85f07b6f62a3f1fe9d4bd8a

Height

#60,106

Difficulty

8.967803

Transactions

4

Size

1.16 KB

Version

2

Bits

08f7c1ee

Nonce

342

Timestamp

7/18/2013, 6:10:31 AM

Confirmations

6,745,078

Merkle Root

7ed1bccd05acb1e965f274a97f76de49276c004f79c0ce35648098edf6649ef9
Transactions (4)
1 in → 1 out12.4500 XPM110 B
2 in → 1 out470.9321 XPM305 B
2 in → 1 out12.5200 XPM308 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.

4.486 × 10⁹⁸(99-digit number)
44865410417294933111…96181397555254993531
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
4.486 × 10⁹⁸(99-digit number)
44865410417294933111…96181397555254993531
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.973 × 10⁹⁸(99-digit number)
89730820834589866223…92362795110509987061
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.794 × 10⁹⁹(100-digit number)
17946164166917973244…84725590221019974121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.589 × 10⁹⁹(100-digit number)
35892328333835946489…69451180442039948241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.178 × 10⁹⁹(100-digit number)
71784656667671892978…38902360884079896481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.435 × 10¹⁰⁰(101-digit number)
14356931333534378595…77804721768159792961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.871 × 10¹⁰⁰(101-digit number)
28713862667068757191…55609443536319585921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.742 × 10¹⁰⁰(101-digit number)
57427725334137514382…11218887072639171841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.148 × 10¹⁰¹(102-digit number)
11485545066827502876…22437774145278343681
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:57,685,542 XPM·at block #6,805,183 · updates every 60s
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