Block #1,143,328

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/7/2015, 10:44:29 AM · Difficulty 10.9293 · 5,681,633 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cc640528b11b3b5d0496e968a79865be8564a271727e484d6eb6826421fa2ed8

Height

#1,143,328

Difficulty

10.929300

Transactions

4

Size

1.15 KB

Version

2

Bits

0aede6a0

Nonce

461,518,777

Timestamp

7/7/2015, 10:44:29 AM

Confirmations

5,681,633

Merkle Root

3db4064aa0bc8b40f58b0f6049ac28bb61b19a5c0becf6f0832af617419be395
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.

1.072 × 10⁹⁸(99-digit number)
10724126887364490560…75586630151208161281
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
1.072 × 10⁹⁸(99-digit number)
10724126887364490560…75586630151208161281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.144 × 10⁹⁸(99-digit number)
21448253774728981120…51173260302416322561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.289 × 10⁹⁸(99-digit number)
42896507549457962241…02346520604832645121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.579 × 10⁹⁸(99-digit number)
85793015098915924483…04693041209665290241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.715 × 10⁹⁹(100-digit number)
17158603019783184896…09386082419330580481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.431 × 10⁹⁹(100-digit number)
34317206039566369793…18772164838661160961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.863 × 10⁹⁹(100-digit number)
68634412079132739586…37544329677322321921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.372 × 10¹⁰⁰(101-digit number)
13726882415826547917…75088659354644643841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.745 × 10¹⁰⁰(101-digit number)
27453764831653095834…50177318709289287681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.490 × 10¹⁰⁰(101-digit number)
54907529663306191669…00354637418578575361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.098 × 10¹⁰¹(102-digit number)
10981505932661238333…00709274837157150721
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,843,768 XPM·at block #6,824,960 · updates every 60s
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