Block #452,152

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/20/2014, 9:45:39 AM · Difficulty 10.3881 · 6,373,370 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e75502530331671252b6c559bf6f5a187f60525c7b7a34971e56b4354d582426

Height

#452,152

Difficulty

10.388102

Transactions

4

Size

2.25 KB

Version

2

Bits

0a635aac

Nonce

103,071

Timestamp

3/20/2014, 9:45:39 AM

Confirmations

6,373,370

Merkle Root

2525b99684f52cb14c7cc8b1df949170704e4c683581cceb7862cdd8a9ac7f07
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.

2.974 × 10⁹⁹(100-digit number)
29741611141531840820…21456341334551449601
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
2.974 × 10⁹⁹(100-digit number)
29741611141531840820…21456341334551449601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.948 × 10⁹⁹(100-digit number)
59483222283063681640…42912682669102899201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.189 × 10¹⁰⁰(101-digit number)
11896644456612736328…85825365338205798401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.379 × 10¹⁰⁰(101-digit number)
23793288913225472656…71650730676411596801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.758 × 10¹⁰⁰(101-digit number)
47586577826450945312…43301461352823193601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.517 × 10¹⁰⁰(101-digit number)
95173155652901890624…86602922705646387201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.903 × 10¹⁰¹(102-digit number)
19034631130580378124…73205845411292774401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.806 × 10¹⁰¹(102-digit number)
38069262261160756249…46411690822585548801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.613 × 10¹⁰¹(102-digit number)
76138524522321512499…92823381645171097601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.522 × 10¹⁰²(103-digit number)
15227704904464302499…85646763290342195201
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:57,848,272 XPM·at block #6,825,521 · updates every 60s
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