Block #445,960

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/16/2014, 6:00:08 AM · Difficulty 10.3593 · 6,365,203 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3365af4f8bedb6499ee4d974a8431a8a0ca53ca01476e006f1b477a766df6f8f

Height

#445,960

Difficulty

10.359333

Transactions

2

Size

2.23 KB

Version

2

Bits

0a5bfd38

Nonce

25,498

Timestamp

3/16/2014, 6:00:08 AM

Confirmations

6,365,203

Merkle Root

97d4939fbda20752790ceafc3f86946eb58effe66a3ccae11232a17c2cc96d27
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.

2.102 × 10¹⁰³(104-digit number)
21025394612592866159…81715531334990151541
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
2.102 × 10¹⁰³(104-digit number)
21025394612592866159…81715531334990151541
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.205 × 10¹⁰³(104-digit number)
42050789225185732318…63431062669980303081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.410 × 10¹⁰³(104-digit number)
84101578450371464636…26862125339960606161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.682 × 10¹⁰⁴(105-digit number)
16820315690074292927…53724250679921212321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.364 × 10¹⁰⁴(105-digit number)
33640631380148585854…07448501359842424641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.728 × 10¹⁰⁴(105-digit number)
67281262760297171709…14897002719684849281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.345 × 10¹⁰⁵(106-digit number)
13456252552059434341…29794005439369698561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.691 × 10¹⁰⁵(106-digit number)
26912505104118868683…59588010878739397121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.382 × 10¹⁰⁵(106-digit number)
53825010208237737367…19176021757478794241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.076 × 10¹⁰⁶(107-digit number)
10765002041647547473…38352043514957588481
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:57,733,416 XPM·at block #6,811,162 · updates every 60s
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