Block #1,361,384

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/8/2015, 9:11:16 PM · Difficulty 10.8419 · 5,448,714 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
69d2bf9f493c301b86c0407247ed382f2cd42742b657bd0cbf7487b7d95c8db1

Height

#1,361,384

Difficulty

10.841872

Transactions

2

Size

3.89 KB

Version

2

Bits

0ad784e8

Nonce

36,248,235

Timestamp

12/8/2015, 9:11:16 PM

Confirmations

5,448,714

Merkle Root

2b2f07f38782035f80caf6b522a6e5adb6d50169ecadac13634614d031bb922d
Transactions (2)
1 in → 1 out8.8000 XPM110 B
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.

7.549 × 10⁹⁵(96-digit number)
75498590097083408965…40287276244350965761
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
7.549 × 10⁹⁵(96-digit number)
75498590097083408965…40287276244350965761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.509 × 10⁹⁶(97-digit number)
15099718019416681793…80574552488701931521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.019 × 10⁹⁶(97-digit number)
30199436038833363586…61149104977403863041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.039 × 10⁹⁶(97-digit number)
60398872077666727172…22298209954807726081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.207 × 10⁹⁷(98-digit number)
12079774415533345434…44596419909615452161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.415 × 10⁹⁷(98-digit number)
24159548831066690868…89192839819230904321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.831 × 10⁹⁷(98-digit number)
48319097662133381737…78385679638461808641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.663 × 10⁹⁷(98-digit number)
96638195324266763475…56771359276923617281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.932 × 10⁹⁸(99-digit number)
19327639064853352695…13542718553847234561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.865 × 10⁹⁸(99-digit number)
38655278129706705390…27085437107694469121
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:57,724,859 XPM·at block #6,810,097 · updates every 60s
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