Block #469,936

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/1/2014, 2:01:05 PM · Difficulty 10.4284 · 6,375,190 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e7a83a1a0b338c8d8e7a49cd169bf07487e01d5b41328ffbdafefe4393650768

Height

#469,936

Difficulty

10.428413

Transactions

2

Size

884 B

Version

2

Bits

0a6dac7e

Nonce

21,067,720

Timestamp

4/1/2014, 2:01:05 PM

Confirmations

6,375,190

Merkle Root

61ee6125e6df027f36b5e7fe927de87289be1ca9285cfd4cc7bf5bb2fef1b017
Transactions (2)
1 in → 1 out9.1900 XPM109 B
5 in → 1 out28.0000 XPM684 B
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.

1.906 × 10⁹⁶(97-digit number)
19061382385051066445…34080552920357068801
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
1.906 × 10⁹⁶(97-digit number)
19061382385051066445…34080552920357068801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.812 × 10⁹⁶(97-digit number)
38122764770102132891…68161105840714137601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.624 × 10⁹⁶(97-digit number)
76245529540204265783…36322211681428275201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.524 × 10⁹⁷(98-digit number)
15249105908040853156…72644423362856550401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.049 × 10⁹⁷(98-digit number)
30498211816081706313…45288846725713100801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.099 × 10⁹⁷(98-digit number)
60996423632163412626…90577693451426201601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.219 × 10⁹⁸(99-digit number)
12199284726432682525…81155386902852403201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.439 × 10⁹⁸(99-digit number)
24398569452865365050…62310773805704806401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.879 × 10⁹⁸(99-digit number)
48797138905730730101…24621547611409612801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.759 × 10⁹⁸(99-digit number)
97594277811461460202…49243095222819225601
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:58,005,435 XPM·at block #6,845,125 · updates every 60s
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