Block #1,101,923

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/12/2015, 10:10:43 PM · Difficulty 10.7594 · 5,722,888 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c38fc80d482b3f1a13982aea9515bb28c85cf9836cea8b5552048f113c280d82

Height

#1,101,923

Difficulty

10.759395

Transactions

2

Size

2.04 KB

Version

2

Bits

0ac267bb

Nonce

2,016,134,100

Timestamp

6/12/2015, 10:10:43 PM

Confirmations

5,722,888

Merkle Root

7879c897cbd86fade77a0be57dfb661535af5f468ba28d1455db0abbe8fd4475
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.

1.346 × 10⁹²(93-digit number)
13463675042021435760…71654695737761427481
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
1.346 × 10⁹²(93-digit number)
13463675042021435760…71654695737761427481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.692 × 10⁹²(93-digit number)
26927350084042871520…43309391475522854961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.385 × 10⁹²(93-digit number)
53854700168085743040…86618782951045709921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.077 × 10⁹³(94-digit number)
10770940033617148608…73237565902091419841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.154 × 10⁹³(94-digit number)
21541880067234297216…46475131804182839681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.308 × 10⁹³(94-digit number)
43083760134468594432…92950263608365679361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.616 × 10⁹³(94-digit number)
86167520268937188864…85900527216731358721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.723 × 10⁹⁴(95-digit number)
17233504053787437772…71801054433462717441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.446 × 10⁹⁴(95-digit number)
34467008107574875545…43602108866925434881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.893 × 10⁹⁴(95-digit number)
68934016215149751091…87204217733850869761
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:57,842,565 XPM·at block #6,824,810 · updates every 60s
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