Block #373,392

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 6:53:22 AM · Difficulty 10.4257 · 6,441,581 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
384dfb650dee07eeffa9ab227be644bd2487737faffd8d989406a6436eb19b6f

Height

#373,392

Difficulty

10.425654

Transactions

1

Size

867 B

Version

2

Bits

0a6cf7aa

Nonce

61,487

Timestamp

1/24/2014, 6:53:22 AM

Confirmations

6,441,581

Merkle Root

01122170b6a2367b0735216f3e74ced16795b6a753a272c8476939918c5e1c63
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.

2.012 × 10⁹⁵(96-digit number)
20124999937770655916…60075394509283294719
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
2.012 × 10⁹⁵(96-digit number)
20124999937770655916…60075394509283294719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.024 × 10⁹⁵(96-digit number)
40249999875541311833…20150789018566589439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.049 × 10⁹⁵(96-digit number)
80499999751082623667…40301578037133178879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.609 × 10⁹⁶(97-digit number)
16099999950216524733…80603156074266357759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.219 × 10⁹⁶(97-digit number)
32199999900433049466…61206312148532715519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.439 × 10⁹⁶(97-digit number)
64399999800866098933…22412624297065431039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.287 × 10⁹⁷(98-digit number)
12879999960173219786…44825248594130862079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.575 × 10⁹⁷(98-digit number)
25759999920346439573…89650497188261724159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.151 × 10⁹⁷(98-digit number)
51519999840692879147…79300994376523448319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.030 × 10⁹⁸(99-digit number)
10303999968138575829…58601988753046896639
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:57,763,870 XPM·at block #6,814,972 · updates every 60s
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