Block #466,549

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/30/2014, 6:24:05 AM · Difficulty 10.4215 · 6,328,009 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c01ba956815b0d7df78407a1985d385faeabdb109f11781e896698695b43f1ed

Height

#466,549

Difficulty

10.421472

Transactions

2

Size

860 B

Version

2

Bits

0a6be59c

Nonce

7,330

Timestamp

3/30/2014, 6:24:05 AM

Confirmations

6,328,009

Merkle Root

efa1b0ed4835df047876e9e0d281788364ed738cc2b5c7ecfcfa43c13ee4ba0d
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.

1.979 × 10⁹⁸(99-digit number)
19793383386344035869…53628452446163406721
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
1.979 × 10⁹⁸(99-digit number)
19793383386344035869…53628452446163406721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.958 × 10⁹⁸(99-digit number)
39586766772688071739…07256904892326813441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.917 × 10⁹⁸(99-digit number)
79173533545376143478…14513809784653626881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.583 × 10⁹⁹(100-digit number)
15834706709075228695…29027619569307253761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.166 × 10⁹⁹(100-digit number)
31669413418150457391…58055239138614507521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.333 × 10⁹⁹(100-digit number)
63338826836300914782…16110478277229015041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.266 × 10¹⁰⁰(101-digit number)
12667765367260182956…32220956554458030081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.533 × 10¹⁰⁰(101-digit number)
25335530734520365913…64441913108916060161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.067 × 10¹⁰⁰(101-digit number)
50671061469040731826…28883826217832120321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.013 × 10¹⁰¹(102-digit number)
10134212293808146365…57767652435664240641
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:57,600,506 XPM·at block #6,794,557 · updates every 60s
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