Block #1,106,658

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/15/2015, 11:37:58 AM · Difficulty 10.8047 · 5,708,394 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
96303f3229b97cacf6f4d236dd0391e2e9c7bb0bf84bfe798524d20582f2d3ca

Height

#1,106,658

Difficulty

10.804672

Transactions

2

Size

916 B

Version

2

Bits

0acdfefe

Nonce

483,279,240

Timestamp

6/15/2015, 11:37:58 AM

Confirmations

5,708,394

Merkle Root

9043a7eb68256839c82ce9a1eb5c9855c93095d4d8a5fc6b633d838e38bd3499
Transactions (2)
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.

5.378 × 10⁹²(93-digit number)
53789566834018405956…69853656466781436351
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
5.378 × 10⁹²(93-digit number)
53789566834018405956…69853656466781436351
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.075 × 10⁹³(94-digit number)
10757913366803681191…39707312933562872701
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.151 × 10⁹³(94-digit number)
21515826733607362382…79414625867125745401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.303 × 10⁹³(94-digit number)
43031653467214724765…58829251734251490801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.606 × 10⁹³(94-digit number)
86063306934429449530…17658503468502981601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.721 × 10⁹⁴(95-digit number)
17212661386885889906…35317006937005963201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.442 × 10⁹⁴(95-digit number)
34425322773771779812…70634013874011926401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.885 × 10⁹⁴(95-digit number)
68850645547543559624…41268027748023852801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.377 × 10⁹⁵(96-digit number)
13770129109508711924…82536055496047705601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.754 × 10⁹⁵(96-digit number)
27540258219017423849…65072110992095411201
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:57,764,507 XPM·at block #6,815,051 · updates every 60s
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