Block #424,001

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/28/2014, 8:30:21 PM · Difficulty 10.3731 · 6,382,238 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e7ae4571daf05dc9d1810bca59c8fdb653665963754278d6d64efa79cbdb2273

Height

#424,001

Difficulty

10.373093

Transactions

2

Size

724 B

Version

2

Bits

0a5f8300

Nonce

95,958

Timestamp

2/28/2014, 8:30:21 PM

Confirmations

6,382,238

Merkle Root

b0985324f6528a5b33b8aafc64b6d201366ab175c3aa63a30bd92d477632b766
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.

7.742 × 10⁹⁹(100-digit number)
77428545398094076547…38547608245412259841
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
7.742 × 10⁹⁹(100-digit number)
77428545398094076547…38547608245412259841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.548 × 10¹⁰⁰(101-digit number)
15485709079618815309…77095216490824519681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.097 × 10¹⁰⁰(101-digit number)
30971418159237630618…54190432981649039361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.194 × 10¹⁰⁰(101-digit number)
61942836318475261237…08380865963298078721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.238 × 10¹⁰¹(102-digit number)
12388567263695052247…16761731926596157441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.477 × 10¹⁰¹(102-digit number)
24777134527390104495…33523463853192314881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.955 × 10¹⁰¹(102-digit number)
49554269054780208990…67046927706384629761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.910 × 10¹⁰¹(102-digit number)
99108538109560417980…34093855412769259521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.982 × 10¹⁰²(103-digit number)
19821707621912083596…68187710825538519041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.964 × 10¹⁰²(103-digit number)
39643415243824167192…36375421651077038081
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,693,992 XPM·at block #6,806,238 · updates every 60s
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