Block #482,700

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/9/2014, 3:37:25 PM · Difficulty 10.5499 · 6,328,156 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
92d5bd93f2d35bbc9828ddb434f01f7aa62e325e7e32908a6255534f57271fea

Height

#482,700

Difficulty

10.549879

Transactions

3

Size

956 B

Version

2

Bits

0a8cc4de

Nonce

206,317,079

Timestamp

4/9/2014, 3:37:25 PM

Confirmations

6,328,156

Merkle Root

16d680d0fe0e36fa99ed61040682e02c0c9dd6145aaa2b71ea63ead51fa63168
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.

8.907 × 10⁹⁹(100-digit number)
89074380540111054836…71054080848613826559
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
8.907 × 10⁹⁹(100-digit number)
89074380540111054836…71054080848613826559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.781 × 10¹⁰⁰(101-digit number)
17814876108022210967…42108161697227653119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.562 × 10¹⁰⁰(101-digit number)
35629752216044421934…84216323394455306239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.125 × 10¹⁰⁰(101-digit number)
71259504432088843868…68432646788910612479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.425 × 10¹⁰¹(102-digit number)
14251900886417768773…36865293577821224959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.850 × 10¹⁰¹(102-digit number)
28503801772835537547…73730587155642449919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.700 × 10¹⁰¹(102-digit number)
57007603545671075095…47461174311284899839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.140 × 10¹⁰²(103-digit number)
11401520709134215019…94922348622569799679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.280 × 10¹⁰²(103-digit number)
22803041418268430038…89844697245139599359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.560 × 10¹⁰²(103-digit number)
45606082836536860076…79689394490279198719
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:57,730,943 XPM·at block #6,810,855 · updates every 60s
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