Block #202,600

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/10/2013, 7:59:22 AM · Difficulty 9.8955 · 6,591,755 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aa4cde3dc8147efa28ff3b5d5e63bc52e4695731f8be882e06c0d3b796c7baf8

Height

#202,600

Difficulty

9.895478

Transactions

5

Size

1.87 KB

Version

2

Bits

09e53e0b

Nonce

18,104

Timestamp

10/10/2013, 7:59:22 AM

Confirmations

6,591,755

Merkle Root

aba940835b7e79b90f14fa287b3df40a88b8e7c82dbb80385fb970eb13b4819c
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.

1.541 × 10⁹⁷(98-digit number)
15412402734732766748…27106056821878533121
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
1.541 × 10⁹⁷(98-digit number)
15412402734732766748…27106056821878533121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.082 × 10⁹⁷(98-digit number)
30824805469465533497…54212113643757066241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.164 × 10⁹⁷(98-digit number)
61649610938931066995…08424227287514132481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.232 × 10⁹⁸(99-digit number)
12329922187786213399…16848454575028264961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.465 × 10⁹⁸(99-digit number)
24659844375572426798…33696909150056529921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.931 × 10⁹⁸(99-digit number)
49319688751144853596…67393818300113059841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.863 × 10⁹⁸(99-digit number)
98639377502289707192…34787636600226119681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.972 × 10⁹⁹(100-digit number)
19727875500457941438…69575273200452239361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.945 × 10⁹⁹(100-digit number)
39455751000915882877…39150546400904478721
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:57,598,874 XPM·at block #6,794,354 · updates every 60s
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