Block #2,836,620

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/12/2018, 10:58:20 PM · Difficulty 11.7163 · 4,005,575 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
daa26f396146cb671a1d72c360afecb7b4a353504c3adedd2757bb097a28868f

Height

#2,836,620

Difficulty

11.716264

Transactions

7

Size

2.33 KB

Version

2

Bits

0bb75d17

Nonce

119,373,870

Timestamp

9/12/2018, 10:58:20 PM

Confirmations

4,005,575

Merkle Root

19a73d942d9c1c6611e781ad8e16a6527788e12cef754e275904df01b9f48c45
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.

4.225 × 10⁹⁵(96-digit number)
42257964105420015651…80382504648521390079
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
4.225 × 10⁹⁵(96-digit number)
42257964105420015651…80382504648521390079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.451 × 10⁹⁵(96-digit number)
84515928210840031303…60765009297042780159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.690 × 10⁹⁶(97-digit number)
16903185642168006260…21530018594085560319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.380 × 10⁹⁶(97-digit number)
33806371284336012521…43060037188171120639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.761 × 10⁹⁶(97-digit number)
67612742568672025042…86120074376342241279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.352 × 10⁹⁷(98-digit number)
13522548513734405008…72240148752684482559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.704 × 10⁹⁷(98-digit number)
27045097027468810017…44480297505368965119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.409 × 10⁹⁷(98-digit number)
54090194054937620034…88960595010737930239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.081 × 10⁹⁸(99-digit number)
10818038810987524006…77921190021475860479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.163 × 10⁹⁸(99-digit number)
21636077621975048013…55842380042951720959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
4.327 × 10⁹⁸(99-digit number)
43272155243950096027…11684760085903441919
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:57,981,953 XPM·at block #6,842,194 · updates every 60s
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