Block #1,097,382

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/9/2015, 7:53:49 PM · Difficulty 10.7552 · 5,708,754 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
31de41f196219b2f321fd103bd2471b8fe91e38f701e2c0a64abbc088b31ed18

Height

#1,097,382

Difficulty

10.755190

Transactions

1

Size

243 B

Version

2

Bits

0ac15424

Nonce

492,132,439

Timestamp

6/9/2015, 7:53:49 PM

Confirmations

5,708,754

Merkle Root

523824b3f50b38f08c6cc2b51c7bd04f72c669c4ded20214c8e5ae98ce9a3d2c
Transactions (1)
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.

3.427 × 10⁹⁶(97-digit number)
34272276499835174167…62921901405408945921
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
3.427 × 10⁹⁶(97-digit number)
34272276499835174167…62921901405408945921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.854 × 10⁹⁶(97-digit number)
68544552999670348335…25843802810817891841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.370 × 10⁹⁷(98-digit number)
13708910599934069667…51687605621635783681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.741 × 10⁹⁷(98-digit number)
27417821199868139334…03375211243271567361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.483 × 10⁹⁷(98-digit number)
54835642399736278668…06750422486543134721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.096 × 10⁹⁸(99-digit number)
10967128479947255733…13500844973086269441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.193 × 10⁹⁸(99-digit number)
21934256959894511467…27001689946172538881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.386 × 10⁹⁸(99-digit number)
43868513919789022934…54003379892345077761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.773 × 10⁹⁸(99-digit number)
87737027839578045869…08006759784690155521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.754 × 10⁹⁹(100-digit number)
17547405567915609173…16013519569380311041
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:57,693,166 XPM·at block #6,806,135 · updates every 60s
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