Block #496,680

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/17/2014, 5:16:15 AM · Difficulty 10.7576 · 6,312,593 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
75972bdc77c796ab06dfd81f9ca961293104d768f5f25d1514ed046a69653228

Height

#496,680

Difficulty

10.757625

Transactions

1

Size

936 B

Version

2

Bits

0ac1f3ae

Nonce

151,705

Timestamp

4/17/2014, 5:16:15 AM

Confirmations

6,312,593

Merkle Root

28bed4f13ef57cebe823195709ac2cad9823c66783869f6e45397bcdd6284643
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.

9.446 × 10⁹⁷(98-digit number)
94468004026866503548…93375724542944915201
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
9.446 × 10⁹⁷(98-digit number)
94468004026866503548…93375724542944915201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.889 × 10⁹⁸(99-digit number)
18893600805373300709…86751449085889830401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.778 × 10⁹⁸(99-digit number)
37787201610746601419…73502898171779660801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.557 × 10⁹⁸(99-digit number)
75574403221493202838…47005796343559321601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.511 × 10⁹⁹(100-digit number)
15114880644298640567…94011592687118643201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.022 × 10⁹⁹(100-digit number)
30229761288597281135…88023185374237286401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.045 × 10⁹⁹(100-digit number)
60459522577194562270…76046370748474572801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.209 × 10¹⁰⁰(101-digit number)
12091904515438912454…52092741496949145601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.418 × 10¹⁰⁰(101-digit number)
24183809030877824908…04185482993898291201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.836 × 10¹⁰⁰(101-digit number)
48367618061755649816…08370965987796582401
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:57,718,252 XPM·at block #6,809,272 · updates every 60s
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