Block #464,514

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/28/2014, 8:10:59 PM · Difficulty 10.4220 · 6,339,680 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
827c983015295035fb06864d42c2cf5695d68936939789d25bfedeb159e3222a

Height

#464,514

Difficulty

10.422007

Transactions

4

Size

961 B

Version

2

Bits

0a6c08a7

Nonce

55,394

Timestamp

3/28/2014, 8:10:59 PM

Confirmations

6,339,680

Merkle Root

c5db44831994bdeab0ab7d59be7dba2ba3fcfd8458e8e85655b99843bea3efba
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.

2.939 × 10⁹⁸(99-digit number)
29396249223118468533…66914464573406309281
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
2.939 × 10⁹⁸(99-digit number)
29396249223118468533…66914464573406309281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.879 × 10⁹⁸(99-digit number)
58792498446236937066…33828929146812618561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.175 × 10⁹⁹(100-digit number)
11758499689247387413…67657858293625237121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.351 × 10⁹⁹(100-digit number)
23516999378494774826…35315716587250474241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.703 × 10⁹⁹(100-digit number)
47033998756989549653…70631433174500948481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.406 × 10⁹⁹(100-digit number)
94067997513979099307…41262866349001896961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.881 × 10¹⁰⁰(101-digit number)
18813599502795819861…82525732698003793921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.762 × 10¹⁰⁰(101-digit number)
37627199005591639722…65051465396007587841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.525 × 10¹⁰⁰(101-digit number)
75254398011183279445…30102930792015175681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.505 × 10¹⁰¹(102-digit number)
15050879602236655889…60205861584030351361
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:57,677,606 XPM·at block #6,804,193 · updates every 60s
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