Block #468,887

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/31/2014, 7:42:44 PM · Difficulty 10.4330 · 6,341,452 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5f1b9b62100620a94d652021df749a965d4e3807c64c4588faf9163072daf0b6

Height

#468,887

Difficulty

10.432986

Transactions

1

Size

1005 B

Version

2

Bits

0a6ed828

Nonce

28,942

Timestamp

3/31/2014, 7:42:44 PM

Confirmations

6,341,452

Merkle Root

3841d3647914928599bd8293ec108d8550220c38c7ce77bf01e467188b9eee44
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.

1.164 × 10¹⁰⁰(101-digit number)
11648759178372663803…54357981665123098881
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
1.164 × 10¹⁰⁰(101-digit number)
11648759178372663803…54357981665123098881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.329 × 10¹⁰⁰(101-digit number)
23297518356745327606…08715963330246197761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.659 × 10¹⁰⁰(101-digit number)
46595036713490655212…17431926660492395521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.319 × 10¹⁰⁰(101-digit number)
93190073426981310424…34863853320984791041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.863 × 10¹⁰¹(102-digit number)
18638014685396262084…69727706641969582081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.727 × 10¹⁰¹(102-digit number)
37276029370792524169…39455413283939164161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.455 × 10¹⁰¹(102-digit number)
74552058741585048339…78910826567878328321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.491 × 10¹⁰²(103-digit number)
14910411748317009667…57821653135756656641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.982 × 10¹⁰²(103-digit number)
29820823496634019335…15643306271513313281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.964 × 10¹⁰²(103-digit number)
59641646993268038671…31286612543026626561
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:57,726,793 XPM·at block #6,810,338 · updates every 60s
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