Block #1,599,832

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/25/2016, 7:08:32 PM · Difficulty 10.6055 · 5,239,574 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
339db25b4e9f3c71a86ee2168b95116781a1e4ccefc76402ce288b4de5c21d63

Height

#1,599,832

Difficulty

10.605477

Transactions

2

Size

1.28 KB

Version

2

Bits

0a9b0087

Nonce

87,729,280

Timestamp

5/25/2016, 7:08:32 PM

Confirmations

5,239,574

Merkle Root

462b7a762b4e5d3456dbe9083769548695e182721e48c20789d7832c6aa74621
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.

9.873 × 10⁹⁶(97-digit number)
98730780218632406857…27255185213638912001
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
9.873 × 10⁹⁶(97-digit number)
98730780218632406857…27255185213638912001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.974 × 10⁹⁷(98-digit number)
19746156043726481371…54510370427277824001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.949 × 10⁹⁷(98-digit number)
39492312087452962742…09020740854555648001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.898 × 10⁹⁷(98-digit number)
78984624174905925485…18041481709111296001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.579 × 10⁹⁸(99-digit number)
15796924834981185097…36082963418222592001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.159 × 10⁹⁸(99-digit number)
31593849669962370194…72165926836445184001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.318 × 10⁹⁸(99-digit number)
63187699339924740388…44331853672890368001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.263 × 10⁹⁹(100-digit number)
12637539867984948077…88663707345780736001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.527 × 10⁹⁹(100-digit number)
25275079735969896155…77327414691561472001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.055 × 10⁹⁹(100-digit number)
50550159471939792311…54654829383122944001
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:57,959,535 XPM·at block #6,839,405 · updates every 60s
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