Block #2,632,994

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/28/2018, 4:47:19 AM · Difficulty 11.1777 · 4,204,426 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
07f6854090695c4db272b77625bdaef08ba9a53c1296aef5c8ebc31e07b9daac

Height

#2,632,994

Difficulty

11.177715

Transactions

3

Size

833 B

Version

2

Bits

0b2d7ec3

Nonce

58,308,667

Timestamp

4/28/2018, 4:47:19 AM

Confirmations

4,204,426

Merkle Root

b7d17307c4d4f54f6f92391ae33cace376b050442989b6b22aa5f1a504a4c047
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.

7.690 × 10⁹⁵(96-digit number)
76902458722915370441…87714386370481226081
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
7.690 × 10⁹⁵(96-digit number)
76902458722915370441…87714386370481226081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.538 × 10⁹⁶(97-digit number)
15380491744583074088…75428772740962452161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.076 × 10⁹⁶(97-digit number)
30760983489166148176…50857545481924904321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.152 × 10⁹⁶(97-digit number)
61521966978332296353…01715090963849808641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.230 × 10⁹⁷(98-digit number)
12304393395666459270…03430181927699617281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.460 × 10⁹⁷(98-digit number)
24608786791332918541…06860363855399234561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.921 × 10⁹⁷(98-digit number)
49217573582665837082…13720727710798469121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.843 × 10⁹⁷(98-digit number)
98435147165331674165…27441455421596938241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.968 × 10⁹⁸(99-digit number)
19687029433066334833…54882910843193876481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.937 × 10⁹⁸(99-digit number)
39374058866132669666…09765821686387752961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
7.874 × 10⁹⁸(99-digit number)
78748117732265339332…19531643372775505921
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:57,943,680 XPM·at block #6,837,419 · updates every 60s
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