Block #455,470

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/22/2014, 2:00:41 PM · Difficulty 10.4117 · 6,340,442 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
863fad52d7f284b45b6ca721817b9c0e88caec42d22ca41103de142710f3b032

Height

#455,470

Difficulty

10.411667

Transactions

1

Size

935 B

Version

2

Bits

0a69630a

Nonce

196,322

Timestamp

3/22/2014, 2:00:41 PM

Confirmations

6,340,442

Merkle Root

b7894571204d560f5045f2539d1fd71458cc5858b6050a5007906c5ba599bc1f
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.

1.528 × 10⁹⁵(96-digit number)
15280697889498713894…11723593093078830321
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
1.528 × 10⁹⁵(96-digit number)
15280697889498713894…11723593093078830321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.056 × 10⁹⁵(96-digit number)
30561395778997427788…23447186186157660641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.112 × 10⁹⁵(96-digit number)
61122791557994855577…46894372372315321281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.222 × 10⁹⁶(97-digit number)
12224558311598971115…93788744744630642561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.444 × 10⁹⁶(97-digit number)
24449116623197942230…87577489489261285121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.889 × 10⁹⁶(97-digit number)
48898233246395884461…75154978978522570241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
9.779 × 10⁹⁶(97-digit number)
97796466492791768923…50309957957045140481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.955 × 10⁹⁷(98-digit number)
19559293298558353784…00619915914090280961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.911 × 10⁹⁷(98-digit number)
39118586597116707569…01239831828180561921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.823 × 10⁹⁷(98-digit number)
78237173194233415139…02479663656361123841
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:57,611,381 XPM·at block #6,795,911 · updates every 60s
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