Block #958,569

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/2/2015, 1:58:32 PM · Difficulty 10.8891 · 5,844,741 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3dd5533bc6e6176d21f2cf02ee8f9ef53084834cd2d2b83929a39b2b86727dd2

Height

#958,569

Difficulty

10.889082

Transactions

4

Size

2.28 KB

Version

2

Bits

0ae39adf

Nonce

207,298,436

Timestamp

3/2/2015, 1:58:32 PM

Confirmations

5,844,741

Merkle Root

cc1604e7c2172bf97143dabc97dc5947c02030b74b49a6d9abb7187d43b1cbe9
Transactions (4)
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.

2.231 × 10⁹⁶(97-digit number)
22319876695200821899…07017978432096940001
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
2.231 × 10⁹⁶(97-digit number)
22319876695200821899…07017978432096940001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.463 × 10⁹⁶(97-digit number)
44639753390401643799…14035956864193880001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.927 × 10⁹⁶(97-digit number)
89279506780803287598…28071913728387760001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.785 × 10⁹⁷(98-digit number)
17855901356160657519…56143827456775520001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.571 × 10⁹⁷(98-digit number)
35711802712321315039…12287654913551040001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.142 × 10⁹⁷(98-digit number)
71423605424642630078…24575309827102080001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.428 × 10⁹⁸(99-digit number)
14284721084928526015…49150619654204160001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.856 × 10⁹⁸(99-digit number)
28569442169857052031…98301239308408320001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.713 × 10⁹⁸(99-digit number)
57138884339714104062…96602478616816640001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.142 × 10⁹⁹(100-digit number)
11427776867942820812…93204957233633280001
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:57,670,508 XPM·at block #6,803,309 · updates every 60s
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