Block #455,564

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/22/2014, 3:22:51 PM · Difficulty 10.4131 · 6,347,942 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
898951b9ec715c387212bc591172e50223984d74fbcb2d57aa83d0703b433814

Height

#455,564

Difficulty

10.413112

Transactions

5

Size

3.96 KB

Version

2

Bits

0a69c1b8

Nonce

83,720

Timestamp

3/22/2014, 3:22:51 PM

Confirmations

6,347,942

Merkle Root

5c425b3660b1049fccce55e4b202a2f832a237261396730e15c527919747c0b5
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.

8.684 × 10¹⁰⁰(101-digit number)
86844190524431443870…42485027535979238321
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
8.684 × 10¹⁰⁰(101-digit number)
86844190524431443870…42485027535979238321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.736 × 10¹⁰¹(102-digit number)
17368838104886288774…84970055071958476641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.473 × 10¹⁰¹(102-digit number)
34737676209772577548…69940110143916953281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.947 × 10¹⁰¹(102-digit number)
69475352419545155096…39880220287833906561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.389 × 10¹⁰²(103-digit number)
13895070483909031019…79760440575667813121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.779 × 10¹⁰²(103-digit number)
27790140967818062038…59520881151335626241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.558 × 10¹⁰²(103-digit number)
55580281935636124077…19041762302671252481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.111 × 10¹⁰³(104-digit number)
11116056387127224815…38083524605342504961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.223 × 10¹⁰³(104-digit number)
22232112774254449630…76167049210685009921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.446 × 10¹⁰³(104-digit number)
44464225548508899261…52334098421370019841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
8.892 × 10¹⁰³(104-digit number)
88928451097017798523…04668196842740039681
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:57,672,072 XPM·at block #6,803,505 · updates every 60s
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