Block #94,173

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/2/2013, 10:12:57 PM · Difficulty 9.2016 · 6,705,180 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cf01c6742d4d77050ce456c16f6d3cadfb601b46b2c7b0a95d11b22084791016

Height

#94,173

Difficulty

9.201610

Transactions

3

Size

922 B

Version

2

Bits

09339cbd

Nonce

90,233

Timestamp

8/2/2013, 10:12:57 PM

Confirmations

6,705,180

Merkle Root

1ff48dd7ca9fcf0d5a1b7f054d32d75eb0552682b8044e37bc734ba939d192be
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.

3.045 × 10¹⁰⁸(109-digit number)
30453183496624953063…52301518438499346241
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
3.045 × 10¹⁰⁸(109-digit number)
30453183496624953063…52301518438499346241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.090 × 10¹⁰⁸(109-digit number)
60906366993249906127…04603036876998692481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.218 × 10¹⁰⁹(110-digit number)
12181273398649981225…09206073753997384961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.436 × 10¹⁰⁹(110-digit number)
24362546797299962450…18412147507994769921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.872 × 10¹⁰⁹(110-digit number)
48725093594599924901…36824295015989539841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.745 × 10¹⁰⁹(110-digit number)
97450187189199849803…73648590031979079681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.949 × 10¹¹⁰(111-digit number)
19490037437839969960…47297180063958159361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.898 × 10¹¹⁰(111-digit number)
38980074875679939921…94594360127916318721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.796 × 10¹¹⁰(111-digit number)
77960149751359879843…89188720255832637441
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:57,638,877 XPM·at block #6,799,352 · updates every 60s
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