Block #1,432,460

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/28/2016, 8:16:41 AM · Difficulty 10.7860 · 5,392,432 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
296a261e6f4e54c2dda50f62edafae8935f4010fe36d9769e34a369eeeb708f1

Height

#1,432,460

Difficulty

10.786041

Transactions

2

Size

1.57 KB

Version

2

Bits

0ac939f4

Nonce

246,609,526

Timestamp

1/28/2016, 8:16:41 AM

Confirmations

5,392,432

Merkle Root

d3f9eaffffde3cff7c55e67551fa4656be50810e80c56b3f03c8770a4be2db8c
Transactions (2)
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.

1.068 × 10⁹⁵(96-digit number)
10683849364681545481…25207631871907708241
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
1.068 × 10⁹⁵(96-digit number)
10683849364681545481…25207631871907708241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.136 × 10⁹⁵(96-digit number)
21367698729363090963…50415263743815416481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.273 × 10⁹⁵(96-digit number)
42735397458726181926…00830527487630832961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.547 × 10⁹⁵(96-digit number)
85470794917452363852…01661054975261665921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.709 × 10⁹⁶(97-digit number)
17094158983490472770…03322109950523331841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.418 × 10⁹⁶(97-digit number)
34188317966980945541…06644219901046663681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.837 × 10⁹⁶(97-digit number)
68376635933961891082…13288439802093327361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.367 × 10⁹⁷(98-digit number)
13675327186792378216…26576879604186654721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.735 × 10⁹⁷(98-digit number)
27350654373584756432…53153759208373309441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.470 × 10⁹⁷(98-digit number)
54701308747169512865…06307518416746618881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.094 × 10⁹⁸(99-digit number)
10940261749433902573…12615036833493237761
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,843,217 XPM·at block #6,824,891 · updates every 60s
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