Block #244,289

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/4/2013, 6:42:00 PM · Difficulty 9.9628 · 6,569,751 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
47bb72f51886b7fd4c6c2edeb2d2fc6d8e8c76995c35a7e7ccab8a32a3d29fef

Height

#244,289

Difficulty

9.962801

Transactions

2

Size

454 B

Version

2

Bits

09f67a20

Nonce

11,094

Timestamp

11/4/2013, 6:42:00 PM

Confirmations

6,569,751

Merkle Root

d5e06a5ae3904c92a2372724264974fd6546ffcde80a942a5a83b6ead1c43bb6
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.

1.025 × 10⁹⁹(100-digit number)
10255015745229561942…49697210063631083521
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
1.025 × 10⁹⁹(100-digit number)
10255015745229561942…49697210063631083521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.051 × 10⁹⁹(100-digit number)
20510031490459123884…99394420127262167041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.102 × 10⁹⁹(100-digit number)
41020062980918247768…98788840254524334081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.204 × 10⁹⁹(100-digit number)
82040125961836495537…97577680509048668161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.640 × 10¹⁰⁰(101-digit number)
16408025192367299107…95155361018097336321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.281 × 10¹⁰⁰(101-digit number)
32816050384734598215…90310722036194672641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.563 × 10¹⁰⁰(101-digit number)
65632100769469196430…80621444072389345281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.312 × 10¹⁰¹(102-digit number)
13126420153893839286…61242888144778690561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.625 × 10¹⁰¹(102-digit number)
26252840307787678572…22485776289557381121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.250 × 10¹⁰¹(102-digit number)
52505680615575357144…44971552579114762241
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:57,756,395 XPM·at block #6,814,039 · updates every 60s
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