Block #1,599,622

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 5/25/2016, 3:05:58 PM · Difficulty 10.6078 · 5,227,693 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7b80df984e80aa7a6531bd2dd986fbfa37e423a0e6c2bd690c715925a884cdf1

Height

#1,599,622

Difficulty

10.607803

Transactions

2

Size

1.51 KB

Version

2

Bits

0a9b98f2

Nonce

1,874,213,534

Timestamp

5/25/2016, 3:05:58 PM

Confirmations

5,227,693

Merkle Root

4583cc5a02647f452d5183f5692654980a18e92ec970fb7e82979428d6155bda
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.

2.490 × 10⁹⁶(97-digit number)
24908784967180157595…52028601277830530561
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
2.490 × 10⁹⁶(97-digit number)
24908784967180157595…52028601277830530561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.981 × 10⁹⁶(97-digit number)
49817569934360315190…04057202555661061121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.963 × 10⁹⁶(97-digit number)
99635139868720630381…08114405111322122241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.992 × 10⁹⁷(98-digit number)
19927027973744126076…16228810222644244481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.985 × 10⁹⁷(98-digit number)
39854055947488252152…32457620445288488961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.970 × 10⁹⁷(98-digit number)
79708111894976504305…64915240890576977921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.594 × 10⁹⁸(99-digit number)
15941622378995300861…29830481781153955841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.188 × 10⁹⁸(99-digit number)
31883244757990601722…59660963562307911681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.376 × 10⁹⁸(99-digit number)
63766489515981203444…19321927124615823361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.275 × 10⁹⁹(100-digit number)
12753297903196240688…38643854249231646721
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:57,862,632 XPM·at block #6,827,314 · updates every 60s
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