Block #2,683,576

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 5/29/2018, 10:22:35 PM · Difficulty 11.6899 · 4,147,182 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1fbbaa6f2633c3b9109e17d36140fc8d189dec9009455334c7b6446a0c0e71b8

Height

#2,683,576

Difficulty

11.689867

Transactions

3

Size

1.04 KB

Version

2

Bits

0bb09b19

Nonce

214,487,201

Timestamp

5/29/2018, 10:22:35 PM

Confirmations

4,147,182

Merkle Root

f3065d45f709a186ef9fd44f869ed1c1be48e12e156e442ef1d29714148e789e
Transactions (3)
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.

1.716 × 10⁹³(94-digit number)
17168591630225607143…73753753027955292159
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
1.716 × 10⁹³(94-digit number)
17168591630225607143…73753753027955292159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.433 × 10⁹³(94-digit number)
34337183260451214287…47507506055910584319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.867 × 10⁹³(94-digit number)
68674366520902428575…95015012111821168639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.373 × 10⁹⁴(95-digit number)
13734873304180485715…90030024223642337279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.746 × 10⁹⁴(95-digit number)
27469746608360971430…80060048447284674559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.493 × 10⁹⁴(95-digit number)
54939493216721942860…60120096894569349119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.098 × 10⁹⁵(96-digit number)
10987898643344388572…20240193789138698239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.197 × 10⁹⁵(96-digit number)
21975797286688777144…40480387578277396479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.395 × 10⁹⁵(96-digit number)
43951594573377554288…80960775156554792959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.790 × 10⁹⁵(96-digit number)
87903189146755108576…61921550313109585919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.758 × 10⁹⁶(97-digit number)
17580637829351021715…23843100626219171839
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:57,890,201 XPM·at block #6,830,757 · updates every 60s
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