Block #1,928,608

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/7/2017, 4:30:16 PM · Difficulty 10.7491 · 4,896,353 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6d3f088982a621f29c1a29e5ead42f16ecc6a80d23d04d6fa721001a17faeb06

Height

#1,928,608

Difficulty

10.749149

Transactions

2

Size

2.30 KB

Version

2

Bits

0abfc837

Nonce

379,226,595

Timestamp

1/7/2017, 4:30:16 PM

Confirmations

4,896,353

Merkle Root

46af2fc42febc15b2ef465625586b5672bfd5b27a223932227457a1a629e03b3
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.

1.208 × 10⁹⁴(95-digit number)
12087477271710561611…85779022808359373921
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
1.208 × 10⁹⁴(95-digit number)
12087477271710561611…85779022808359373921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.417 × 10⁹⁴(95-digit number)
24174954543421123223…71558045616718747841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.834 × 10⁹⁴(95-digit number)
48349909086842246446…43116091233437495681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.669 × 10⁹⁴(95-digit number)
96699818173684492893…86232182466874991361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.933 × 10⁹⁵(96-digit number)
19339963634736898578…72464364933749982721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.867 × 10⁹⁵(96-digit number)
38679927269473797157…44928729867499965441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.735 × 10⁹⁵(96-digit number)
77359854538947594315…89857459734999930881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.547 × 10⁹⁶(97-digit number)
15471970907789518863…79714919469999861761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.094 × 10⁹⁶(97-digit number)
30943941815579037726…59429838939999723521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.188 × 10⁹⁶(97-digit number)
61887883631158075452…18859677879999447041
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,843,768 XPM·at block #6,824,960 · updates every 60s
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