Block #360,424

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/15/2014, 11:03:06 AM · Difficulty 10.3917 · 6,449,404 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
699997253c11789c432601907a56f5ec0591813dc31c23fff0f6404c86839dda

Height

#360,424

Difficulty

10.391732

Transactions

1

Size

1.05 KB

Version

2

Bits

0a644890

Nonce

96,669

Timestamp

1/15/2014, 11:03:06 AM

Confirmations

6,449,404

Merkle Root

4b7af24731d0557dd4b93d6e8711495d8f5b51d7b3696775664fd750cd0695ff
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.

7.799 × 10⁹⁴(95-digit number)
77994830373576369012…28336280258924944001
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
7.799 × 10⁹⁴(95-digit number)
77994830373576369012…28336280258924944001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.559 × 10⁹⁵(96-digit number)
15598966074715273802…56672560517849888001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.119 × 10⁹⁵(96-digit number)
31197932149430547604…13345121035699776001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.239 × 10⁹⁵(96-digit number)
62395864298861095209…26690242071399552001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.247 × 10⁹⁶(97-digit number)
12479172859772219041…53380484142799104001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.495 × 10⁹⁶(97-digit number)
24958345719544438083…06760968285598208001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.991 × 10⁹⁶(97-digit number)
49916691439088876167…13521936571196416001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.983 × 10⁹⁶(97-digit number)
99833382878177752335…27043873142392832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.996 × 10⁹⁷(98-digit number)
19966676575635550467…54087746284785664001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.993 × 10⁹⁷(98-digit number)
39933353151271100934…08175492569571328001
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:57,722,709 XPM·at block #6,809,827 · updates every 60s
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