Block #1,412,036

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/13/2016, 8:06:29 PM · Difficulty 10.8044 · 5,392,968 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
594013469e7846f1c28314f047379347589fad7ceefcc27f03d224ea27cb3764

Height

#1,412,036

Difficulty

10.804370

Transactions

2

Size

801 B

Version

2

Bits

0acdeb34

Nonce

749,766,206

Timestamp

1/13/2016, 8:06:29 PM

Confirmations

5,392,968

Merkle Root

f497787583e02fff90579aa11b62ded48672dfb38d611e17874659d4cc3baf5f
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.

1.951 × 10⁹⁵(96-digit number)
19517575284997181044…72719430839053769601
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
1.951 × 10⁹⁵(96-digit number)
19517575284997181044…72719430839053769601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.903 × 10⁹⁵(96-digit number)
39035150569994362089…45438861678107539201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.807 × 10⁹⁵(96-digit number)
78070301139988724179…90877723356215078401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.561 × 10⁹⁶(97-digit number)
15614060227997744835…81755446712430156801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.122 × 10⁹⁶(97-digit number)
31228120455995489671…63510893424860313601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.245 × 10⁹⁶(97-digit number)
62456240911990979343…27021786849720627201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.249 × 10⁹⁷(98-digit number)
12491248182398195868…54043573699441254401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.498 × 10⁹⁷(98-digit number)
24982496364796391737…08087147398882508801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.996 × 10⁹⁷(98-digit number)
49964992729592783474…16174294797765017601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.992 × 10⁹⁷(98-digit number)
99929985459185566949…32348589595530035201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.998 × 10⁹⁸(99-digit number)
19985997091837113389…64697179191060070401
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:57,684,100 XPM·at block #6,805,003 · updates every 60s
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