Block #2,485,966

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/23/2018, 7:00:59 AM · Difficulty 10.9679 · 4,355,192 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8476797f746411fbb6720f3ceb51be869f1ac0dba444477b7030bb3bffda85b9

Height

#2,485,966

Difficulty

10.967892

Transactions

19

Size

5.96 KB

Version

2

Bits

0af7c7c1

Nonce

141,638,599

Timestamp

1/23/2018, 7:00:59 AM

Confirmations

4,355,192

Merkle Root

5c140fe6fca8b989c87f3eaf164eb48215f864f7662b1ee88a7b3b17afdac212
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.

3.203 × 10⁹³(94-digit number)
32037940698589267481…63914701565931822079
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
3.203 × 10⁹³(94-digit number)
32037940698589267481…63914701565931822079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.407 × 10⁹³(94-digit number)
64075881397178534963…27829403131863644159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.281 × 10⁹⁴(95-digit number)
12815176279435706992…55658806263727288319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.563 × 10⁹⁴(95-digit number)
25630352558871413985…11317612527454576639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.126 × 10⁹⁴(95-digit number)
51260705117742827970…22635225054909153279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.025 × 10⁹⁵(96-digit number)
10252141023548565594…45270450109818306559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.050 × 10⁹⁵(96-digit number)
20504282047097131188…90540900219636613119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.100 × 10⁹⁵(96-digit number)
41008564094194262376…81081800439273226239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.201 × 10⁹⁵(96-digit number)
82017128188388524753…62163600878546452479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.640 × 10⁹⁶(97-digit number)
16403425637677704950…24327201757092904959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
3.280 × 10⁹⁶(97-digit number)
32806851275355409901…48654403514185809919
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,973,628 XPM·at block #6,841,157 · updates every 60s
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