Block #1,395,892

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/2/2016, 11:24:39 AM · Difficulty 10.8121 · 5,420,735 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a393dbc0616f52092c046972df2c46f464b36c5b16f39a7a9016cf43b17504f

Height

#1,395,892

Difficulty

10.812068

Transactions

2

Size

2.01 KB

Version

2

Bits

0acfe3af

Nonce

1,935,139,999

Timestamp

1/2/2016, 11:24:39 AM

Confirmations

5,420,735

Merkle Root

acbc9b05b69e38d09825387f72f8e44b0e0e744a21dfc3c05318c3bc7dc04e44
Transactions (2)
1 in → 1 out8.6000 XPM110 B
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.

1.025 × 10⁹²(93-digit number)
10254882526475264775…27801244339187810361
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
1.025 × 10⁹²(93-digit number)
10254882526475264775…27801244339187810361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.050 × 10⁹²(93-digit number)
20509765052950529551…55602488678375620721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.101 × 10⁹²(93-digit number)
41019530105901059102…11204977356751241441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.203 × 10⁹²(93-digit number)
82039060211802118204…22409954713502482881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.640 × 10⁹³(94-digit number)
16407812042360423640…44819909427004965761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.281 × 10⁹³(94-digit number)
32815624084720847281…89639818854009931521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.563 × 10⁹³(94-digit number)
65631248169441694563…79279637708019863041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.312 × 10⁹⁴(95-digit number)
13126249633888338912…58559275416039726081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.625 × 10⁹⁴(95-digit number)
26252499267776677825…17118550832079452161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.250 × 10⁹⁴(95-digit number)
52504998535553355650…34237101664158904321
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:57,777,137 XPM·at block #6,816,626 · updates every 60s
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