Block #1,106,278

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/15/2015, 8:50:11 AM · Difficulty 10.7963 · 5,708,785 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3651eb968dc6da5353dcb427514dbfe54c83d129c7fe4653a591a8c072c7f15d

Height

#1,106,278

Difficulty

10.796294

Transactions

3

Size

24.05 KB

Version

2

Bits

0acbd9f3

Nonce

1,076,767,915

Timestamp

6/15/2015, 8:50:11 AM

Confirmations

5,708,785

Merkle Root

7a21874543e675f144efb64a8c4c94f228c69cfe1adfd5056a5a8149df2b23dc
Transactions (3)
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.

2.164 × 10⁹⁶(97-digit number)
21648724769715854455…90218120206635724801
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
2.164 × 10⁹⁶(97-digit number)
21648724769715854455…90218120206635724801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.329 × 10⁹⁶(97-digit number)
43297449539431708910…80436240413271449601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.659 × 10⁹⁶(97-digit number)
86594899078863417820…60872480826542899201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.731 × 10⁹⁷(98-digit number)
17318979815772683564…21744961653085798401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.463 × 10⁹⁷(98-digit number)
34637959631545367128…43489923306171596801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.927 × 10⁹⁷(98-digit number)
69275919263090734256…86979846612343193601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.385 × 10⁹⁸(99-digit number)
13855183852618146851…73959693224686387201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.771 × 10⁹⁸(99-digit number)
27710367705236293702…47919386449372774401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.542 × 10⁹⁸(99-digit number)
55420735410472587404…95838772898745548801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.108 × 10⁹⁹(100-digit number)
11084147082094517480…91677545797491097601
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:57,764,595 XPM·at block #6,815,062 · updates every 60s
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