Block #1,194,815

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/15/2015, 2:14:29 AM · Difficulty 10.8422 · 5,621,392 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e178a7f5e605de90b5d9f12ee59a5664e47e1b953de75168348737bc6184f27e

Height

#1,194,815

Difficulty

10.842192

Transactions

2

Size

5.19 KB

Version

2

Bits

0ad799e3

Nonce

263,372,987

Timestamp

8/15/2015, 2:14:29 AM

Confirmations

5,621,392

Merkle Root

74b9e3b525c2496475c42c78e8adc3842e25a4572986b2d092738ccd4864d1d6
Transactions (2)
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.

2.354 × 10⁹⁴(95-digit number)
23542721392760057985…13609658103671065009
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
2.354 × 10⁹⁴(95-digit number)
23542721392760057985…13609658103671065009
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.708 × 10⁹⁴(95-digit number)
47085442785520115971…27219316207342130019
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.417 × 10⁹⁴(95-digit number)
94170885571040231942…54438632414684260039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.883 × 10⁹⁵(96-digit number)
18834177114208046388…08877264829368520079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.766 × 10⁹⁵(96-digit number)
37668354228416092776…17754529658737040159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.533 × 10⁹⁵(96-digit number)
75336708456832185553…35509059317474080319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.506 × 10⁹⁶(97-digit number)
15067341691366437110…71018118634948160639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.013 × 10⁹⁶(97-digit number)
30134683382732874221…42036237269896321279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.026 × 10⁹⁶(97-digit number)
60269366765465748443…84072474539792642559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.205 × 10⁹⁷(98-digit number)
12053873353093149688…68144949079585285119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.410 × 10⁹⁷(98-digit number)
24107746706186299377…36289898159170570239
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,773,783 XPM·at block #6,816,206 · updates every 60s
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