Block #793,370

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/2/2014, 6:44:55 AM · Difficulty 10.9741 · 6,010,084 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d72f53050e6ddb1e0ccf6898614899f300c13324915131e4999f4283baf303c0

Height

#793,370

Difficulty

10.974129

Transactions

3

Size

658 B

Version

2

Bits

0af96081

Nonce

78,812,247

Timestamp

11/2/2014, 6:44:55 AM

Confirmations

6,010,084

Merkle Root

7c7fda3421006e18d6c7d52d0bdaadb5c19e6bc74860c1d7187967a7eb9df2a4
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.

1.393 × 10⁹⁶(97-digit number)
13932078780511131934…02969470071994899199
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
1.393 × 10⁹⁶(97-digit number)
13932078780511131934…02969470071994899199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.786 × 10⁹⁶(97-digit number)
27864157561022263868…05938940143989798399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.572 × 10⁹⁶(97-digit number)
55728315122044527736…11877880287979596799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.114 × 10⁹⁷(98-digit number)
11145663024408905547…23755760575959193599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.229 × 10⁹⁷(98-digit number)
22291326048817811094…47511521151918387199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.458 × 10⁹⁷(98-digit number)
44582652097635622188…95023042303836774399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.916 × 10⁹⁷(98-digit number)
89165304195271244377…90046084607673548799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.783 × 10⁹⁸(99-digit number)
17833060839054248875…80092169215347097599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.566 × 10⁹⁸(99-digit number)
35666121678108497751…60184338430694195199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.133 × 10⁹⁸(99-digit number)
71332243356216995502…20368676861388390399
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,671,659 XPM·at block #6,803,453 · updates every 60s
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