Block #453,361

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/21/2014, 5:51:09 AM · Difficulty 10.3894 · 6,352,621 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5763715d9d7c74ab366a84514a9f41d9f950bfca92299f13b31a9df082b0ee47

Height

#453,361

Difficulty

10.389432

Transactions

2

Size

543 B

Version

2

Bits

0a63b1ca

Nonce

146,181

Timestamp

3/21/2014, 5:51:09 AM

Confirmations

6,352,621

Merkle Root

df11522d6d741810bda9c95131d2b5cbcef951ba5c1a38becf92f66c40589daa
Transactions (2)
1 in → 1 out9.2600 XPM110 B
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.

2.971 × 10¹⁰¹(102-digit number)
29710305581206263200…49193472122167241601
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
2.971 × 10¹⁰¹(102-digit number)
29710305581206263200…49193472122167241601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.942 × 10¹⁰¹(102-digit number)
59420611162412526400…98386944244334483201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.188 × 10¹⁰²(103-digit number)
11884122232482505280…96773888488668966401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.376 × 10¹⁰²(103-digit number)
23768244464965010560…93547776977337932801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.753 × 10¹⁰²(103-digit number)
47536488929930021120…87095553954675865601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.507 × 10¹⁰²(103-digit number)
95072977859860042240…74191107909351731201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.901 × 10¹⁰³(104-digit number)
19014595571972008448…48382215818703462401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.802 × 10¹⁰³(104-digit number)
38029191143944016896…96764431637406924801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.605 × 10¹⁰³(104-digit number)
76058382287888033792…93528863274813849601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.521 × 10¹⁰⁴(105-digit number)
15211676457577606758…87057726549627699201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.042 × 10¹⁰⁴(105-digit number)
30423352915155213517…74115453099255398401
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:57,691,933 XPM·at block #6,805,981 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.