Block #953,283

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/26/2015, 6:53:14 PM · Difficulty 10.8928 · 5,848,530 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e046ac825797a43f6b7140e354098ce5c6524ac391ba7434ede8ad0ef91fe481

Height

#953,283

Difficulty

10.892820

Transactions

4

Size

886 B

Version

2

Bits

0ae48fd2

Nonce

626,450,100

Timestamp

2/26/2015, 6:53:14 PM

Confirmations

5,848,530

Merkle Root

a908c1f4319c09b0e9a197c8c0be596a2b4c7fa16cfa79a4864a1cad6ac12cad
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.

7.808 × 10⁹⁵(96-digit number)
78081909498162808420…21926107217318184641
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
7.808 × 10⁹⁵(96-digit number)
78081909498162808420…21926107217318184641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.561 × 10⁹⁶(97-digit number)
15616381899632561684…43852214434636369281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.123 × 10⁹⁶(97-digit number)
31232763799265123368…87704428869272738561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.246 × 10⁹⁶(97-digit number)
62465527598530246736…75408857738545477121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.249 × 10⁹⁷(98-digit number)
12493105519706049347…50817715477090954241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.498 × 10⁹⁷(98-digit number)
24986211039412098694…01635430954181908481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.997 × 10⁹⁷(98-digit number)
49972422078824197389…03270861908363816961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.994 × 10⁹⁷(98-digit number)
99944844157648394778…06541723816727633921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.998 × 10⁹⁸(99-digit number)
19988968831529678955…13083447633455267841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.997 × 10⁹⁸(99-digit number)
39977937663059357911…26166895266910535681
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:57,658,596 XPM·at block #6,801,812 · updates every 60s
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