Block #1,062,812

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/17/2015, 3:51:43 AM · Difficulty 10.7291 · 5,742,195 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
50563dcd4df2d683118c3c16246b5283f1c0dd03c27d5b8a4b6944e7f8ff90e6

Height

#1,062,812

Difficulty

10.729065

Transactions

3

Size

1.08 KB

Version

2

Bits

0abaa409

Nonce

15,285,124

Timestamp

5/17/2015, 3:51:43 AM

Confirmations

5,742,195

Merkle Root

1d8c203db11d3ca236c74b36b2a2ffb6e54fddd65b5ccefddab2b96097bdcc28
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.

6.773 × 10⁹⁸(99-digit number)
67737594592590458896…33386850260399882241
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
6.773 × 10⁹⁸(99-digit number)
67737594592590458896…33386850260399882241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.354 × 10⁹⁹(100-digit number)
13547518918518091779…66773700520799764481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.709 × 10⁹⁹(100-digit number)
27095037837036183558…33547401041599528961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.419 × 10⁹⁹(100-digit number)
54190075674072367116…67094802083199057921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.083 × 10¹⁰⁰(101-digit number)
10838015134814473423…34189604166398115841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.167 × 10¹⁰⁰(101-digit number)
21676030269628946846…68379208332796231681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.335 × 10¹⁰⁰(101-digit number)
43352060539257893693…36758416665592463361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.670 × 10¹⁰⁰(101-digit number)
86704121078515787386…73516833331184926721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.734 × 10¹⁰¹(102-digit number)
17340824215703157477…47033666662369853441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.468 × 10¹⁰¹(102-digit number)
34681648431406314954…94067333324739706881
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:57,684,125 XPM·at block #6,805,006 · updates every 60s
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