Block #2,855,192

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/26/2018, 12:24:55 AM · Difficulty 11.7034 · 3,975,596 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e0d09821d84cce3c0fd318593845178f3ce130e255a97e735059897d14853235

Height

#2,855,192

Difficulty

11.703364

Transactions

11

Size

2.31 KB

Version

2

Bits

0bb40faf

Nonce

94,422,476

Timestamp

9/26/2018, 12:24:55 AM

Confirmations

3,975,596

Merkle Root

62345261ab40d203b999b334c43ddfe47d5e0f3af569aac3c05bc55b01d2c0cf
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.

2.352 × 10⁹²(93-digit number)
23526452862226717607…23350612344441002079
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
2.352 × 10⁹²(93-digit number)
23526452862226717607…23350612344441002079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.705 × 10⁹²(93-digit number)
47052905724453435214…46701224688882004159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.410 × 10⁹²(93-digit number)
94105811448906870429…93402449377764008319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.882 × 10⁹³(94-digit number)
18821162289781374085…86804898755528016639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.764 × 10⁹³(94-digit number)
37642324579562748171…73609797511056033279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.528 × 10⁹³(94-digit number)
75284649159125496343…47219595022112066559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.505 × 10⁹⁴(95-digit number)
15056929831825099268…94439190044224133119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.011 × 10⁹⁴(95-digit number)
30113859663650198537…88878380088448266239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.022 × 10⁹⁴(95-digit number)
60227719327300397074…77756760176896532479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.204 × 10⁹⁵(96-digit number)
12045543865460079414…55513520353793064959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.409 × 10⁹⁵(96-digit number)
24091087730920158829…11027040707586129919
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:57,890,441 XPM·at block #6,830,787 · updates every 60s
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