Block #1,514,450

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/27/2016, 11:02:40 AM · Difficulty 10.6057 · 5,302,865 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2844b39880ae395f9d79326f7779075d40a78c4b0ccd53caa7a174aca97f2793

Height

#1,514,450

Difficulty

10.605716

Transactions

2

Size

1.04 KB

Version

2

Bits

0a9b103c

Nonce

464,283,779

Timestamp

3/27/2016, 11:02:40 AM

Confirmations

5,302,865

Merkle Root

371ea575981b765d27bd2b18874f26138be5a0c821b0cd7219f49d15786c7312
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.

1.063 × 10⁹²(93-digit number)
10636679710716105666…78961133082365975521
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
1.063 × 10⁹²(93-digit number)
10636679710716105666…78961133082365975521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.127 × 10⁹²(93-digit number)
21273359421432211332…57922266164731951041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.254 × 10⁹²(93-digit number)
42546718842864422664…15844532329463902081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.509 × 10⁹²(93-digit number)
85093437685728845329…31689064658927804161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.701 × 10⁹³(94-digit number)
17018687537145769065…63378129317855608321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.403 × 10⁹³(94-digit number)
34037375074291538131…26756258635711216641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.807 × 10⁹³(94-digit number)
68074750148583076263…53512517271422433281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.361 × 10⁹⁴(95-digit number)
13614950029716615252…07025034542844866561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.722 × 10⁹⁴(95-digit number)
27229900059433230505…14050069085689733121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.445 × 10⁹⁴(95-digit number)
54459800118866461010…28100138171379466241
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:57,782,565 XPM·at block #6,817,314 · updates every 60s
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