Block #1,371,758

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/16/2015, 5:21:26 PM · Difficulty 10.8109 · 5,468,026 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a1ce147624670585e9bc88b18d1aaadfd3938637d8fe7360471fea61299dea6

Height

#1,371,758

Difficulty

10.810890

Transactions

2

Size

5.33 KB

Version

2

Bits

0acf9685

Nonce

10,214,538

Timestamp

12/16/2015, 5:21:26 PM

Confirmations

5,468,026

Merkle Root

c28a491620fe74bb3c026825523a0ed608d3b1d217b1b452a8fe7a017c25c5f1
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.

4.316 × 10⁹⁶(97-digit number)
43160398510559412691…67411725264839168001
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
4.316 × 10⁹⁶(97-digit number)
43160398510559412691…67411725264839168001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.632 × 10⁹⁶(97-digit number)
86320797021118825383…34823450529678336001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.726 × 10⁹⁷(98-digit number)
17264159404223765076…69646901059356672001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.452 × 10⁹⁷(98-digit number)
34528318808447530153…39293802118713344001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.905 × 10⁹⁷(98-digit number)
69056637616895060306…78587604237426688001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.381 × 10⁹⁸(99-digit number)
13811327523379012061…57175208474853376001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.762 × 10⁹⁸(99-digit number)
27622655046758024122…14350416949706752001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.524 × 10⁹⁸(99-digit number)
55245310093516048245…28700833899413504001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.104 × 10⁹⁹(100-digit number)
11049062018703209649…57401667798827008001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.209 × 10⁹⁹(100-digit number)
22098124037406419298…14803335597654016001
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:57,962,562 XPM·at block #6,839,783 · updates every 60s
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