Block #1,526,051

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/4/2016, 1:03:39 PM · Difficulty 10.6032 · 5,300,146 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3a6b4f57c1c181b68c19460bf58fa01d1e2c79cfcde8440eae73fc675c98ff22

Height

#1,526,051

Difficulty

10.603166

Transactions

3

Size

2.11 KB

Version

2

Bits

0a9a6917

Nonce

13,947,723

Timestamp

4/4/2016, 1:03:39 PM

Confirmations

5,300,146

Merkle Root

3d5b7984ba120b15be3f26108f24066e08bdaae2f61d545f7afba4db34c38576
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.

1.676 × 10⁹⁴(95-digit number)
16761256958194439725…56312064208913886041
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
1.676 × 10⁹⁴(95-digit number)
16761256958194439725…56312064208913886041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.352 × 10⁹⁴(95-digit number)
33522513916388879451…12624128417827772081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.704 × 10⁹⁴(95-digit number)
67045027832777758903…25248256835655544161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.340 × 10⁹⁵(96-digit number)
13409005566555551780…50496513671311088321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.681 × 10⁹⁵(96-digit number)
26818011133111103561…00993027342622176641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.363 × 10⁹⁵(96-digit number)
53636022266222207123…01986054685244353281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.072 × 10⁹⁶(97-digit number)
10727204453244441424…03972109370488706561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.145 × 10⁹⁶(97-digit number)
21454408906488882849…07944218740977413121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.290 × 10⁹⁶(97-digit number)
42908817812977765698…15888437481954826241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
8.581 × 10⁹⁶(97-digit number)
85817635625955531396…31776874963909652481
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:57,853,705 XPM·at block #6,826,196 · updates every 60s
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