Block #373,427

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 7:29:37 AM · Difficulty 10.4254 · 6,436,955 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
305988f4c4cc8977a8ea726a3954500c13c949de6889f304adbdc8c140d69fea

Height

#373,427

Difficulty

10.425375

Transactions

1

Size

968 B

Version

2

Bits

0a6ce560

Nonce

64,068

Timestamp

1/24/2014, 7:29:37 AM

Confirmations

6,436,955

Merkle Root

58569b0b83365c13ebc5364adf08c3e5f0e11e5c6e72717919a0f1dfe211f303
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.

7.949 × 10⁹¹(92-digit number)
79499228628286132808…59183560328963564321
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
7.949 × 10⁹¹(92-digit number)
79499228628286132808…59183560328963564321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.589 × 10⁹²(93-digit number)
15899845725657226561…18367120657927128641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.179 × 10⁹²(93-digit number)
31799691451314453123…36734241315854257281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.359 × 10⁹²(93-digit number)
63599382902628906247…73468482631708514561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.271 × 10⁹³(94-digit number)
12719876580525781249…46936965263417029121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.543 × 10⁹³(94-digit number)
25439753161051562498…93873930526834058241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.087 × 10⁹³(94-digit number)
50879506322103124997…87747861053668116481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.017 × 10⁹⁴(95-digit number)
10175901264420624999…75495722107336232961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.035 × 10⁹⁴(95-digit number)
20351802528841249999…50991444214672465921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.070 × 10⁹⁴(95-digit number)
40703605057682499998…01982888429344931841
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:57,727,134 XPM·at block #6,810,381 · updates every 60s
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