Block #1,566,903

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/1/2016, 4:49:50 AM · Difficulty 10.7584 · 5,247,578 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
caae1dd421ec6fa55c4a72043339d1d7c320fc45f6ac5041da2029e4c534fe4f

Height

#1,566,903

Difficulty

10.758362

Transactions

3

Size

1.50 KB

Version

2

Bits

0ac22409

Nonce

435,211,174

Timestamp

5/1/2016, 4:49:50 AM

Confirmations

5,247,578

Merkle Root

2223b47c4f3b7b8b285570e4fc7098589d9b62fc147f4198ec250f1226841767
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.

5.920 × 10⁹³(94-digit number)
59205802929225148334…91492355905297485531
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
5.920 × 10⁹³(94-digit number)
59205802929225148334…91492355905297485531
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.184 × 10⁹⁴(95-digit number)
11841160585845029666…82984711810594971061
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.368 × 10⁹⁴(95-digit number)
23682321171690059333…65969423621189942121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.736 × 10⁹⁴(95-digit number)
47364642343380118667…31938847242379884241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.472 × 10⁹⁴(95-digit number)
94729284686760237335…63877694484759768481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.894 × 10⁹⁵(96-digit number)
18945856937352047467…27755388969519536961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.789 × 10⁹⁵(96-digit number)
37891713874704094934…55510777939039073921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.578 × 10⁹⁵(96-digit number)
75783427749408189868…11021555878078147841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.515 × 10⁹⁶(97-digit number)
15156685549881637973…22043111756156295681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.031 × 10⁹⁶(97-digit number)
30313371099763275947…44086223512312591361
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:57,759,924 XPM·at block #6,814,480 · updates every 60s
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