Block #594,017

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/19/2014, 4:55:49 AM · Difficulty 10.9390 · 6,220,795 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ac0c57af0761390c7a0b127a94807570060253cdd9a3637171718bb4d1c9bfb2

Height

#594,017

Difficulty

10.939047

Transactions

1

Size

698 B

Version

2

Bits

0af06564

Nonce

98,877

Timestamp

6/19/2014, 4:55:49 AM

Confirmations

6,220,795

Merkle Root

3677aac7a7282b792c99dde2ea110a21d6c26ca2d98e780d50c8a05535bba8d2
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.

4.110 × 10⁹⁷(98-digit number)
41103228459754375334…89237628260062863361
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
4.110 × 10⁹⁷(98-digit number)
41103228459754375334…89237628260062863361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.220 × 10⁹⁷(98-digit number)
82206456919508750668…78475256520125726721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.644 × 10⁹⁸(99-digit number)
16441291383901750133…56950513040251453441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.288 × 10⁹⁸(99-digit number)
32882582767803500267…13901026080502906881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.576 × 10⁹⁸(99-digit number)
65765165535607000535…27802052161005813761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.315 × 10⁹⁹(100-digit number)
13153033107121400107…55604104322011627521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.630 × 10⁹⁹(100-digit number)
26306066214242800214…11208208644023255041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.261 × 10⁹⁹(100-digit number)
52612132428485600428…22416417288046510081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.052 × 10¹⁰⁰(101-digit number)
10522426485697120085…44832834576093020161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.104 × 10¹⁰⁰(101-digit number)
21044852971394240171…89665669152186040321
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:57,762,582 XPM·at block #6,814,811 · updates every 60s
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