Block #1,453,190

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/12/2016, 2:03:31 PM · Difficulty 10.7285 · 5,391,547 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
82ba84adcf24081ebfe1a6a6dfb122a5cd7da5370617e15022c0b7dece315aba

Height

#1,453,190

Difficulty

10.728528

Transactions

2

Size

1.15 KB

Version

2

Bits

0aba80cd

Nonce

246,355,243

Timestamp

2/12/2016, 2:03:31 PM

Confirmations

5,391,547

Merkle Root

f808839dfa1e66fd50b5358ae909a3eddf48b4af29ef5231c36b8e1ba85d9375
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.

1.102 × 10⁹⁴(95-digit number)
11021930387941571900…94254315417039067019
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
1.102 × 10⁹⁴(95-digit number)
11021930387941571900…94254315417039067019
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.204 × 10⁹⁴(95-digit number)
22043860775883143801…88508630834078134039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.408 × 10⁹⁴(95-digit number)
44087721551766287602…77017261668156268079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.817 × 10⁹⁴(95-digit number)
88175443103532575205…54034523336312536159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.763 × 10⁹⁵(96-digit number)
17635088620706515041…08069046672625072319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.527 × 10⁹⁵(96-digit number)
35270177241413030082…16138093345250144639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.054 × 10⁹⁵(96-digit number)
70540354482826060164…32276186690500289279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.410 × 10⁹⁶(97-digit number)
14108070896565212032…64552373381000578559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.821 × 10⁹⁶(97-digit number)
28216141793130424065…29104746762001157119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.643 × 10⁹⁶(97-digit number)
56432283586260848131…58209493524002314239
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:58,002,307 XPM·at block #6,844,736 · updates every 60s
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