Block #600,618

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/24/2014, 9:36:08 PM · Difficulty 10.9165 · 6,207,546 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
428c9606d390647fa79ccc302da8e920a45aac52aecb63126a04b2599d8aba31

Height

#600,618

Difficulty

10.916541

Transactions

1

Size

529 B

Version

2

Bits

0aeaa26f

Nonce

129,856

Timestamp

6/24/2014, 9:36:08 PM

Confirmations

6,207,546

Merkle Root

c4d840e27247160c0bb3851ccb69a1d6242604c8102b94fb172571221864f950
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.

6.917 × 10⁹⁹(100-digit number)
69179030684603392302…47434794132626317121
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
6.917 × 10⁹⁹(100-digit number)
69179030684603392302…47434794132626317121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.383 × 10¹⁰⁰(101-digit number)
13835806136920678460…94869588265252634241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.767 × 10¹⁰⁰(101-digit number)
27671612273841356921…89739176530505268481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.534 × 10¹⁰⁰(101-digit number)
55343224547682713842…79478353061010536961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.106 × 10¹⁰¹(102-digit number)
11068644909536542768…58956706122021073921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.213 × 10¹⁰¹(102-digit number)
22137289819073085536…17913412244042147841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.427 × 10¹⁰¹(102-digit number)
44274579638146171073…35826824488084295681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.854 × 10¹⁰¹(102-digit number)
88549159276292342147…71653648976168591361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.770 × 10¹⁰²(103-digit number)
17709831855258468429…43307297952337182721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.541 × 10¹⁰²(103-digit number)
35419663710516936859…86614595904674365441
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:57,709,358 XPM·at block #6,808,163 · updates every 60s
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