Block #1,102,478

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/13/2015, 7:35:32 AM · Difficulty 10.7589 · 5,714,371 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2edc95e7254be5acecd4a7b3aa79162f7baded042952984c5b10027a85f7128

Height

#1,102,478

Difficulty

10.758939

Transactions

2

Size

581 B

Version

2

Bits

0ac249d9

Nonce

2,402,043,876

Timestamp

6/13/2015, 7:35:32 AM

Confirmations

5,714,371

Merkle Root

4b7130679dcec54a98de273de98a54203ca9c0ba27257a1127f6098d48e52908
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.

2.581 × 10⁹⁷(98-digit number)
25811773669512818616…14043769751770393601
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
2.581 × 10⁹⁷(98-digit number)
25811773669512818616…14043769751770393601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.162 × 10⁹⁷(98-digit number)
51623547339025637232…28087539503540787201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.032 × 10⁹⁸(99-digit number)
10324709467805127446…56175079007081574401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.064 × 10⁹⁸(99-digit number)
20649418935610254893…12350158014163148801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.129 × 10⁹⁸(99-digit number)
41298837871220509786…24700316028326297601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.259 × 10⁹⁸(99-digit number)
82597675742441019572…49400632056652595201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.651 × 10⁹⁹(100-digit number)
16519535148488203914…98801264113305190401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.303 × 10⁹⁹(100-digit number)
33039070296976407828…97602528226610380801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.607 × 10⁹⁹(100-digit number)
66078140593952815657…95205056453220761601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.321 × 10¹⁰⁰(101-digit number)
13215628118790563131…90410112906441523201
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:57,778,834 XPM·at block #6,816,848 · updates every 60s
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