Block #919,091

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/1/2015, 9:32:39 PM · Difficulty 10.9214 · 5,885,118 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1a828d751934bb23a3b245ab8e1f64426f554a1f0a151c3d52e568d8b4467afc

Height

#919,091

Difficulty

10.921441

Transactions

5

Size

7.12 KB

Version

2

Bits

0aebe396

Nonce

1,453,106,238

Timestamp

2/1/2015, 9:32:39 PM

Confirmations

5,885,118

Merkle Root

78fe1e8133108b5c0efe5691fe6bb772c254842147fe0fc4c3c3dc8462425d2a
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.

1.618 × 10⁹⁶(97-digit number)
16189637876504196886…59007827728265802879
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
1.618 × 10⁹⁶(97-digit number)
16189637876504196886…59007827728265802879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.237 × 10⁹⁶(97-digit number)
32379275753008393773…18015655456531605759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.475 × 10⁹⁶(97-digit number)
64758551506016787546…36031310913063211519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.295 × 10⁹⁷(98-digit number)
12951710301203357509…72062621826126423039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.590 × 10⁹⁷(98-digit number)
25903420602406715018…44125243652252846079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.180 × 10⁹⁷(98-digit number)
51806841204813430037…88250487304505692159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.036 × 10⁹⁸(99-digit number)
10361368240962686007…76500974609011384319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.072 × 10⁹⁸(99-digit number)
20722736481925372014…53001949218022768639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.144 × 10⁹⁸(99-digit number)
41445472963850744029…06003898436045537279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.289 × 10⁹⁸(99-digit number)
82890945927701488059…12007796872091074559
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:57,677,719 XPM·at block #6,804,208 · updates every 60s
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