Block #922,323

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 9:35:01 AM · Difficulty 10.9156 · 5,870,581 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ae124d169304e7327a616d6c84f9c40844a064871a346b8f60f97567923bb831

Height

#922,323

Difficulty

10.915575

Transactions

5

Size

115.97 KB

Version

2

Bits

0aea631e

Nonce

373,582,146

Timestamp

2/4/2015, 9:35:01 AM

Confirmations

5,870,581

Merkle Root

296c1793cb07fbfab7169a86c1a170cc34a735866b83a65505d914282bbab66f
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1198.5711 XPM28.94 KB
200 in → 1 out997.5812 XPM28.94 KB
200 in → 1 out1112.4940 XPM28.94 KB
200 in → 1 out1085.0358 XPM28.94 KB
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.

8.376 × 10⁹⁶(97-digit number)
83766357819110439118…49650204889302380801
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
8.376 × 10⁹⁶(97-digit number)
83766357819110439118…49650204889302380801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.675 × 10⁹⁷(98-digit number)
16753271563822087823…99300409778604761601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.350 × 10⁹⁷(98-digit number)
33506543127644175647…98600819557209523201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.701 × 10⁹⁷(98-digit number)
67013086255288351294…97201639114419046401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.340 × 10⁹⁸(99-digit number)
13402617251057670258…94403278228838092801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.680 × 10⁹⁸(99-digit number)
26805234502115340517…88806556457676185601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.361 × 10⁹⁸(99-digit number)
53610469004230681035…77613112915352371201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.072 × 10⁹⁹(100-digit number)
10722093800846136207…55226225830704742401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.144 × 10⁹⁹(100-digit number)
21444187601692272414…10452451661409484801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.288 × 10⁹⁹(100-digit number)
42888375203384544828…20904903322818969601
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:57,587,209 XPM·at block #6,792,903 · updates every 60s
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