Block #3,094,376

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 3/15/2019, 3:06:12 PM · Difficulty 11.0674 · 3,739,602 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51d361c4cb7f841c8862a144c330dff3fcea1fb982d655d3a3fa06be45c2a5a5

Height

#3,094,376

Difficulty

11.067427

Transactions

21

Size

6.21 KB

Version

2

Bits

0b1142e2

Nonce

1,791,237,587

Timestamp

3/15/2019, 3:06:12 PM

Confirmations

3,739,602

Merkle Root

4410eb369d5d8f68bf1a9666295f696e2bfc0cf591da54224bd0a39b4a423f7a
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.

6.292 × 10⁹⁶(97-digit number)
62928111213380658570…19565510155828686079
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
6.292 × 10⁹⁶(97-digit number)
62928111213380658570…19565510155828686079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.258 × 10⁹⁷(98-digit number)
12585622242676131714…39131020311657372159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.517 × 10⁹⁷(98-digit number)
25171244485352263428…78262040623314744319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.034 × 10⁹⁷(98-digit number)
50342488970704526856…56524081246629488639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.006 × 10⁹⁸(99-digit number)
10068497794140905371…13048162493258977279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.013 × 10⁹⁸(99-digit number)
20136995588281810742…26096324986517954559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.027 × 10⁹⁸(99-digit number)
40273991176563621485…52192649973035909119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.054 × 10⁹⁸(99-digit number)
80547982353127242970…04385299946071818239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.610 × 10⁹⁹(100-digit number)
16109596470625448594…08770599892143636479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.221 × 10⁹⁹(100-digit number)
32219192941250897188…17541199784287272959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
6.443 × 10⁹⁹(100-digit number)
64438385882501794376…35082399568574545919
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:57,916,048 XPM·at block #6,833,977 · updates every 60s
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