Block #1,528,391

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/6/2016, 3:03:54 AM · Difficulty 10.6081 · 5,308,182 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b8ca9055360aaca093a4f577c02a47c5d6f9c36ad44127723c8e5487810d1b26

Height

#1,528,391

Difficulty

10.608122

Transactions

2

Size

934 B

Version

2

Bits

0a9badea

Nonce

764,699

Timestamp

4/6/2016, 3:03:54 AM

Confirmations

5,308,182

Merkle Root

fd5b7794ab10294f84d4dc023bfc3a44cffb79392965a277f3252db98e5f1d1f
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.

9.063 × 10⁹⁴(95-digit number)
90634783334690375716…72970996084215142401
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
9.063 × 10⁹⁴(95-digit number)
90634783334690375716…72970996084215142401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.812 × 10⁹⁵(96-digit number)
18126956666938075143…45941992168430284801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.625 × 10⁹⁵(96-digit number)
36253913333876150286…91883984336860569601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.250 × 10⁹⁵(96-digit number)
72507826667752300572…83767968673721139201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.450 × 10⁹⁶(97-digit number)
14501565333550460114…67535937347442278401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.900 × 10⁹⁶(97-digit number)
29003130667100920229…35071874694884556801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.800 × 10⁹⁶(97-digit number)
58006261334201840458…70143749389769113601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.160 × 10⁹⁷(98-digit number)
11601252266840368091…40287498779538227201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.320 × 10⁹⁷(98-digit number)
23202504533680736183…80574997559076454401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.640 × 10⁹⁷(98-digit number)
46405009067361472366…61149995118152908801
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:57,936,849 XPM·at block #6,836,572 · updates every 60s
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