Block #2,376,779

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/12/2017, 8:40:33 PM · Difficulty 10.8813 · 4,468,303 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3611f14e3aab532c2eb70929e54fc4999fa11ac9f201d50b65ea6791ca00fdd9

Height

#2,376,779

Difficulty

10.881350

Transactions

3

Size

1.36 KB

Version

2

Bits

0ae1a020

Nonce

947,191,684

Timestamp

11/12/2017, 8:40:33 PM

Confirmations

4,468,303

Merkle Root

9ef154aef0575dc2ff83361d69f5dd10b7bad9487a3a432f6787ae63ed1d53cf
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.

2.644 × 10⁹⁶(97-digit number)
26449577019412822877…67378726467181534719
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
2.644 × 10⁹⁶(97-digit number)
26449577019412822877…67378726467181534719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.289 × 10⁹⁶(97-digit number)
52899154038825645755…34757452934363069439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.057 × 10⁹⁷(98-digit number)
10579830807765129151…69514905868726138879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.115 × 10⁹⁷(98-digit number)
21159661615530258302…39029811737452277759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.231 × 10⁹⁷(98-digit number)
42319323231060516604…78059623474904555519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.463 × 10⁹⁷(98-digit number)
84638646462121033209…56119246949809111039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.692 × 10⁹⁸(99-digit number)
16927729292424206641…12238493899618222079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.385 × 10⁹⁸(99-digit number)
33855458584848413283…24476987799236444159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.771 × 10⁹⁸(99-digit number)
67710917169696826567…48953975598472888319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.354 × 10⁹⁹(100-digit number)
13542183433939365313…97907951196945776639
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:58,005,083 XPM·at block #6,845,081 · updates every 60s
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