Block #471,894

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/2/2014, 9:25:44 PM · Difficulty 10.4387 · 6,353,643 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
646949e8cf1df632c5d0edf510d9ce25a147ea71014d11b477c79212184bf908

Height

#471,894

Difficulty

10.438701

Transactions

5

Size

1.44 KB

Version

2

Bits

0a704eae

Nonce

33,508

Timestamp

4/2/2014, 9:25:44 PM

Confirmations

6,353,643

Merkle Root

2566568b08cfaffef33662af2d80a28147b6b5c02ce9da150586384b59421977
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.

1.261 × 10¹⁰²(103-digit number)
12610726925061577218…68201033873590693801
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
1.261 × 10¹⁰²(103-digit number)
12610726925061577218…68201033873590693801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.522 × 10¹⁰²(103-digit number)
25221453850123154436…36402067747181387601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.044 × 10¹⁰²(103-digit number)
50442907700246308873…72804135494362775201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.008 × 10¹⁰³(104-digit number)
10088581540049261774…45608270988725550401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.017 × 10¹⁰³(104-digit number)
20177163080098523549…91216541977451100801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.035 × 10¹⁰³(104-digit number)
40354326160197047099…82433083954902201601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.070 × 10¹⁰³(104-digit number)
80708652320394094198…64866167909804403201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.614 × 10¹⁰⁴(105-digit number)
16141730464078818839…29732335819608806401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.228 × 10¹⁰⁴(105-digit number)
32283460928157637679…59464671639217612801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.456 × 10¹⁰⁴(105-digit number)
64566921856315275358…18929343278435225601
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:57,848,394 XPM·at block #6,825,536 · updates every 60s
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