Block #1,446,352

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/7/2016, 10:03:41 AM · Difficulty 10.7589 · 5,380,806 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
dc97942b206b0a1a7a06f24d3655e33bcb0f025edff622fc581e4ab26df692f4

Height

#1,446,352

Difficulty

10.758875

Transactions

3

Size

1.20 KB

Version

2

Bits

0ac2459e

Nonce

1,039,311,807

Timestamp

2/7/2016, 10:03:41 AM

Confirmations

5,380,806

Merkle Root

3d599c6e2c9ccf93551eb22c72d3b00c22e13c19b1ae1e19be681cd6ec6e549a
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.

1.017 × 10⁹⁴(95-digit number)
10177985507673853303…35421651346937734291
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
1.017 × 10⁹⁴(95-digit number)
10177985507673853303…35421651346937734291
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.035 × 10⁹⁴(95-digit number)
20355971015347706606…70843302693875468581
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.071 × 10⁹⁴(95-digit number)
40711942030695413213…41686605387750937161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.142 × 10⁹⁴(95-digit number)
81423884061390826426…83373210775501874321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.628 × 10⁹⁵(96-digit number)
16284776812278165285…66746421551003748641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.256 × 10⁹⁵(96-digit number)
32569553624556330570…33492843102007497281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.513 × 10⁹⁵(96-digit number)
65139107249112661141…66985686204014994561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.302 × 10⁹⁶(97-digit number)
13027821449822532228…33971372408029989121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.605 × 10⁹⁶(97-digit number)
26055642899645064456…67942744816059978241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.211 × 10⁹⁶(97-digit number)
52111285799290128912…35885489632119956481
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:57,861,448 XPM·at block #6,827,157 · updates every 60s
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