Block #436,625

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 3/9/2014, 5:33:44 PM · Difficulty 10.3601 · 6,372,898 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
94fa499fa45767abed406c1abf771d470c287a778535bc82d48f462b9b09cb40

Height

#436,625

Difficulty

10.360096

Transactions

1

Size

902 B

Version

2

Bits

0a5c2f46

Nonce

5,513

Timestamp

3/9/2014, 5:33:44 PM

Confirmations

6,372,898

Merkle Root

f19131fafbb76d8f85a1e1395a73bafc33b428d49ddccbe143dd8949aeaa3c99
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.

6.900 × 10⁹⁶(97-digit number)
69008785485640926438…05662882008071069049
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
6.900 × 10⁹⁶(97-digit number)
69008785485640926438…05662882008071069049
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.380 × 10⁹⁷(98-digit number)
13801757097128185287…11325764016142138099
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.760 × 10⁹⁷(98-digit number)
27603514194256370575…22651528032284276199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.520 × 10⁹⁷(98-digit number)
55207028388512741151…45303056064568552399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.104 × 10⁹⁸(99-digit number)
11041405677702548230…90606112129137104799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.208 × 10⁹⁸(99-digit number)
22082811355405096460…81212224258274209599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.416 × 10⁹⁸(99-digit number)
44165622710810192920…62424448516548419199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.833 × 10⁹⁸(99-digit number)
88331245421620385841…24848897033096838399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.766 × 10⁹⁹(100-digit number)
17666249084324077168…49697794066193676799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.533 × 10⁹⁹(100-digit number)
35332498168648154336…99395588132387353599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.066 × 10⁹⁹(100-digit number)
70664996337296308673…98791176264774707199
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:57,720,261 XPM·at block #6,809,522 · updates every 60s
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