Block #932,364

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/11/2015, 9:17:38 PM · Difficulty 10.9026 · 5,877,149 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d32499bbd6c9083dc9ab0fd3533ee5666b30d85c49ce79b7d456f9daf4e819f2

Height

#932,364

Difficulty

10.902588

Transactions

4

Size

2.74 KB

Version

2

Bits

0ae7100a

Nonce

347,542,178

Timestamp

2/11/2015, 9:17:38 PM

Confirmations

5,877,149

Merkle Root

c90e674fcc17d9b39017d278dbb44c4f0f688788f206fff849f61f4ac8d97150
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.

2.244 × 10⁹⁴(95-digit number)
22445776037357056141…06943709628083908801
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
2.244 × 10⁹⁴(95-digit number)
22445776037357056141…06943709628083908801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.489 × 10⁹⁴(95-digit number)
44891552074714112283…13887419256167817601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.978 × 10⁹⁴(95-digit number)
89783104149428224567…27774838512335635201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.795 × 10⁹⁵(96-digit number)
17956620829885644913…55549677024671270401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.591 × 10⁹⁵(96-digit number)
35913241659771289827…11099354049342540801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.182 × 10⁹⁵(96-digit number)
71826483319542579654…22198708098685081601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.436 × 10⁹⁶(97-digit number)
14365296663908515930…44397416197370163201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.873 × 10⁹⁶(97-digit number)
28730593327817031861…88794832394740326401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.746 × 10⁹⁶(97-digit number)
57461186655634063723…77589664789480652801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.149 × 10⁹⁷(98-digit number)
11492237331126812744…55179329578961305601
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:57,720,179 XPM·at block #6,809,512 · updates every 60s
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