Block #2,946,167

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/30/2018, 4:55:46 PM · Difficulty 11.3967 · 3,895,161 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6ad8068c15c04a39ad474ff6b5ed3c6468e43043fecf70a0cf45ec1a4f23330a

Height

#2,946,167

Difficulty

11.396739

Transactions

2

Size

392 B

Version

2

Bits

0b6590ae

Nonce

199,903,906

Timestamp

11/30/2018, 4:55:46 PM

Confirmations

3,895,161

Merkle Root

d59d5c5b053ad7bd92bc6195b741a6862db4f893a442e557419cd07054fee6f9
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.

2.978 × 10⁹⁵(96-digit number)
29783213353236937558…15719751334064583041
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
2.978 × 10⁹⁵(96-digit number)
29783213353236937558…15719751334064583041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.956 × 10⁹⁵(96-digit number)
59566426706473875117…31439502668129166081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.191 × 10⁹⁶(97-digit number)
11913285341294775023…62879005336258332161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.382 × 10⁹⁶(97-digit number)
23826570682589550046…25758010672516664321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.765 × 10⁹⁶(97-digit number)
47653141365179100093…51516021345033328641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.530 × 10⁹⁶(97-digit number)
95306282730358200187…03032042690066657281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.906 × 10⁹⁷(98-digit number)
19061256546071640037…06064085380133314561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.812 × 10⁹⁷(98-digit number)
38122513092143280074…12128170760266629121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.624 × 10⁹⁷(98-digit number)
76245026184286560149…24256341520533258241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.524 × 10⁹⁸(99-digit number)
15249005236857312029…48512683041066516481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.049 × 10⁹⁸(99-digit number)
30498010473714624059…97025366082133032961
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:57,974,987 XPM·at block #6,841,327 · updates every 60s
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