Block #1,189,296

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 8/10/2015, 12:58:23 PM · Difficulty 10.8713 · 5,623,248 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91ff9d7230a6bdb25b880c82dd0357bcbada8543bac07b66f9f0efc0bac5960e

Height

#1,189,296

Difficulty

10.871348

Transactions

3

Size

3.89 KB

Version

2

Bits

0adf10a5

Nonce

931,508,239

Timestamp

8/10/2015, 12:58:23 PM

Confirmations

5,623,248

Merkle Root

44d95d18b31162c36f562c83edc7c5c01d68d3437d71b78b97fde90104ed714f
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.

5.323 × 10⁹⁴(95-digit number)
53238762318189867163…48738722340708584839
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
5.323 × 10⁹⁴(95-digit number)
53238762318189867163…48738722340708584839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.064 × 10⁹⁵(96-digit number)
10647752463637973432…97477444681417169679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.129 × 10⁹⁵(96-digit number)
21295504927275946865…94954889362834339359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.259 × 10⁹⁵(96-digit number)
42591009854551893730…89909778725668678719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.518 × 10⁹⁵(96-digit number)
85182019709103787461…79819557451337357439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.703 × 10⁹⁶(97-digit number)
17036403941820757492…59639114902674714879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.407 × 10⁹⁶(97-digit number)
34072807883641514984…19278229805349429759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.814 × 10⁹⁶(97-digit number)
68145615767283029969…38556459610698859519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.362 × 10⁹⁷(98-digit number)
13629123153456605993…77112919221397719039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.725 × 10⁹⁷(98-digit number)
27258246306913211987…54225838442795438079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.451 × 10⁹⁷(98-digit number)
54516492613826423975…08451676885590876159
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:57,744,383 XPM·at block #6,812,543 · updates every 60s
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