Block #455,407

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/22/2014, 1:21:00 PM · Difficulty 10.4090 · 6,371,316 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b28aace5d7fe1d8bb8729f4b900ecda0fd662f07007ba8b1c79a28917cebddaa

Height

#455,407

Difficulty

10.408965

Transactions

1

Size

901 B

Version

2

Bits

0a68b1ed

Nonce

35,472

Timestamp

3/22/2014, 1:21:00 PM

Confirmations

6,371,316

Merkle Root

378bec45d139040a62da61577232c57a5f5096f434ef02d2506419e609f9ee24
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.

1.953 × 10⁹⁴(95-digit number)
19535358161070258334…19968172555766516481
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
1.953 × 10⁹⁴(95-digit number)
19535358161070258334…19968172555766516481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.907 × 10⁹⁴(95-digit number)
39070716322140516668…39936345111533032961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.814 × 10⁹⁴(95-digit number)
78141432644281033337…79872690223066065921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.562 × 10⁹⁵(96-digit number)
15628286528856206667…59745380446132131841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.125 × 10⁹⁵(96-digit number)
31256573057712413334…19490760892264263681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.251 × 10⁹⁵(96-digit number)
62513146115424826669…38981521784528527361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.250 × 10⁹⁶(97-digit number)
12502629223084965333…77963043569057054721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.500 × 10⁹⁶(97-digit number)
25005258446169930667…55926087138114109441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.001 × 10⁹⁶(97-digit number)
50010516892339861335…11852174276228218881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.000 × 10⁹⁷(98-digit number)
10002103378467972267…23704348552456437761
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:57,857,938 XPM·at block #6,826,722 · updates every 60s
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