Block #2,468,526

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/11/2018, 9:12:49 PM · Difficulty 10.9602 · 4,373,083 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c31daa4e853e556bfc6d41b3b54eb82b31e5f907cb9f6f84adea7af49a64f71e

Height

#2,468,526

Difficulty

10.960173

Transactions

8

Size

2.52 KB

Version

2

Bits

0af5cdde

Nonce

510,556,624

Timestamp

1/11/2018, 9:12:49 PM

Confirmations

4,373,083

Merkle Root

dbc0da1b175a52ca101aabee125f84cd6da61d5d6b50109a1999b8ca485a3a98
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.

3.532 × 10⁹⁶(97-digit number)
35325685662043130830…64738126668155330561
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
3.532 × 10⁹⁶(97-digit number)
35325685662043130830…64738126668155330561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.065 × 10⁹⁶(97-digit number)
70651371324086261660…29476253336310661121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.413 × 10⁹⁷(98-digit number)
14130274264817252332…58952506672621322241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.826 × 10⁹⁷(98-digit number)
28260548529634504664…17905013345242644481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.652 × 10⁹⁷(98-digit number)
56521097059269009328…35810026690485288961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.130 × 10⁹⁸(99-digit number)
11304219411853801865…71620053380970577921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.260 × 10⁹⁸(99-digit number)
22608438823707603731…43240106761941155841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.521 × 10⁹⁸(99-digit number)
45216877647415207462…86480213523882311681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.043 × 10⁹⁸(99-digit number)
90433755294830414925…72960427047764623361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.808 × 10⁹⁹(100-digit number)
18086751058966082985…45920854095529246721
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:57,977,259 XPM·at block #6,841,608 · updates every 60s
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