Block #484,520

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 2:22:04 PM · Difficulty 10.5890 · 6,328,313 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
29e7b59a6bb4edfc52c6c652b4393288e0efd6169f6cf32dc1d46d087c84cb8d

Height

#484,520

Difficulty

10.589023

Transactions

3

Size

1.22 KB

Version

2

Bits

0a96ca2e

Nonce

9,734

Timestamp

4/10/2014, 2:22:04 PM

Confirmations

6,328,313

Merkle Root

de68cb4c77c62900ccff6c703cebf5666a53cd45327ee57a72bbb0fb61e7c0e5
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.

3.175 × 10¹⁰³(104-digit number)
31753443556794184437…54248047975560859521
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
3.175 × 10¹⁰³(104-digit number)
31753443556794184437…54248047975560859521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.350 × 10¹⁰³(104-digit number)
63506887113588368875…08496095951121719041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.270 × 10¹⁰⁴(105-digit number)
12701377422717673775…16992191902243438081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.540 × 10¹⁰⁴(105-digit number)
25402754845435347550…33984383804486876161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.080 × 10¹⁰⁴(105-digit number)
50805509690870695100…67968767608973752321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.016 × 10¹⁰⁵(106-digit number)
10161101938174139020…35937535217947504641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.032 × 10¹⁰⁵(106-digit number)
20322203876348278040…71875070435895009281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.064 × 10¹⁰⁵(106-digit number)
40644407752696556080…43750140871790018561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.128 × 10¹⁰⁵(106-digit number)
81288815505393112160…87500281743580037121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.625 × 10¹⁰⁶(107-digit number)
16257763101078622432…75000563487160074241
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:57,746,708 XPM·at block #6,812,832 · updates every 60s
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