Block #905,043

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2015, 9:11:32 AM · Difficulty 10.9364 · 5,890,850 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2875b974bc76f496cede7a0f68eccb3e5873ba92c8a3617f8167c893f1a3be39

Height

#905,043

Difficulty

10.936358

Transactions

4

Size

1.16 KB

Version

2

Bits

0aefb52b

Nonce

1,924,216,040

Timestamp

1/22/2015, 9:11:32 AM

Confirmations

5,890,850

Merkle Root

992086a3da7ba3d7d227d3eee0c0486e944d2af23a2ed990d1aab3645199a3d6
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.

2.189 × 10⁹⁷(98-digit number)
21895460400624146398…25960564745599385601
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
2.189 × 10⁹⁷(98-digit number)
21895460400624146398…25960564745599385601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.379 × 10⁹⁷(98-digit number)
43790920801248292797…51921129491198771201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.758 × 10⁹⁷(98-digit number)
87581841602496585595…03842258982397542401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.751 × 10⁹⁸(99-digit number)
17516368320499317119…07684517964795084801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.503 × 10⁹⁸(99-digit number)
35032736640998634238…15369035929590169601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.006 × 10⁹⁸(99-digit number)
70065473281997268476…30738071859180339201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.401 × 10⁹⁹(100-digit number)
14013094656399453695…61476143718360678401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.802 × 10⁹⁹(100-digit number)
28026189312798907390…22952287436721356801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.605 × 10⁹⁹(100-digit number)
56052378625597814781…45904574873442713601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.121 × 10¹⁰⁰(101-digit number)
11210475725119562956…91809149746885427201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.242 × 10¹⁰⁰(101-digit number)
22420951450239125912…83618299493770854401
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,611,227 XPM·at block #6,795,892 · updates every 60s
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