Block #1,975,060

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/8/2017, 8:41:00 PM · Difficulty 10.7568 · 4,842,828 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0ac845695ff73d7a2b4b0264229357b6fb24838cbdf828791ba9513f754690ca

Height

#1,975,060

Difficulty

10.756799

Transactions

2

Size

3.54 KB

Version

2

Bits

0ac1bd95

Nonce

28,268,511

Timestamp

2/8/2017, 8:41:00 PM

Confirmations

4,842,828

Merkle Root

32765dc9a1e367c2c654ec21071b5d67c73dfd043022a26c2c0b055fc3db74fd
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.

2.151 × 10⁹⁵(96-digit number)
21519605675378031544…15370858542057571519
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
2.151 × 10⁹⁵(96-digit number)
21519605675378031544…15370858542057571519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.303 × 10⁹⁵(96-digit number)
43039211350756063088…30741717084115143039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.607 × 10⁹⁵(96-digit number)
86078422701512126177…61483434168230286079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.721 × 10⁹⁶(97-digit number)
17215684540302425235…22966868336460572159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.443 × 10⁹⁶(97-digit number)
34431369080604850471…45933736672921144319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.886 × 10⁹⁶(97-digit number)
68862738161209700942…91867473345842288639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.377 × 10⁹⁷(98-digit number)
13772547632241940188…83734946691684577279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.754 × 10⁹⁷(98-digit number)
27545095264483880376…67469893383369154559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.509 × 10⁹⁷(98-digit number)
55090190528967760753…34939786766738309119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.101 × 10⁹⁸(99-digit number)
11018038105793552150…69879573533476618239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.203 × 10⁹⁸(99-digit number)
22036076211587104301…39759147066953236479
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:57,787,164 XPM·at block #6,817,887 · updates every 60s
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