Block #1,490,834

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/10/2016, 6:05:53 AM · Difficulty 10.6861 · 5,352,356 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5f34581490311077608364fab8502f7b4da23c5350e084d8d3629fbc0dddf7d1

Height

#1,490,834

Difficulty

10.686077

Transactions

2

Size

900 B

Version

2

Bits

0aafa2bd

Nonce

1,908,424,640

Timestamp

3/10/2016, 6:05:53 AM

Confirmations

5,352,356

Merkle Root

b455090adb0f781e9a0144e4a2f433ad004794c3074bc978a989618fe4de707a
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.

6.284 × 10⁹⁴(95-digit number)
62842754767334640365…20839354895794912421
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
6.284 × 10⁹⁴(95-digit number)
62842754767334640365…20839354895794912421
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.256 × 10⁹⁵(96-digit number)
12568550953466928073…41678709791589824841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.513 × 10⁹⁵(96-digit number)
25137101906933856146…83357419583179649681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.027 × 10⁹⁵(96-digit number)
50274203813867712292…66714839166359299361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.005 × 10⁹⁶(97-digit number)
10054840762773542458…33429678332718598721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.010 × 10⁹⁶(97-digit number)
20109681525547084916…66859356665437197441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.021 × 10⁹⁶(97-digit number)
40219363051094169833…33718713330874394881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.043 × 10⁹⁶(97-digit number)
80438726102188339667…67437426661748789761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.608 × 10⁹⁷(98-digit number)
16087745220437667933…34874853323497579521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.217 × 10⁹⁷(98-digit number)
32175490440875335866…69749706646995159041
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:57,989,889 XPM·at block #6,843,189 · updates every 60s
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