Block #485,905

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/11/2014, 8:06:25 AM · Difficulty 10.6145 · 6,359,225 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
280f6d84cdad5eaa03c08e101e5c0b29e9fe5fca280b5b830620f2b1146c349e

Height

#485,905

Difficulty

10.614523

Transactions

2

Size

581 B

Version

2

Bits

0a9d5163

Nonce

46,054,396

Timestamp

4/11/2014, 8:06:25 AM

Confirmations

6,359,225

Merkle Root

f4a1ebe3d351daeb9a2751ab60ad257d48633f700b70ed5046882e703549145b
Transactions (2)
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.

3.924 × 10⁹⁸(99-digit number)
39247771743831347828…92399091890913253439
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
3.924 × 10⁹⁸(99-digit number)
39247771743831347828…92399091890913253439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.849 × 10⁹⁸(99-digit number)
78495543487662695657…84798183781826506879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.569 × 10⁹⁹(100-digit number)
15699108697532539131…69596367563653013759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.139 × 10⁹⁹(100-digit number)
31398217395065078263…39192735127306027519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.279 × 10⁹⁹(100-digit number)
62796434790130156526…78385470254612055039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.255 × 10¹⁰⁰(101-digit number)
12559286958026031305…56770940509224110079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.511 × 10¹⁰⁰(101-digit number)
25118573916052062610…13541881018448220159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.023 × 10¹⁰⁰(101-digit number)
50237147832104125220…27083762036896440319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.004 × 10¹⁰¹(102-digit number)
10047429566420825044…54167524073792880639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.009 × 10¹⁰¹(102-digit number)
20094859132841650088…08335048147585761279
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:58,005,468 XPM·at block #6,845,129 · updates every 60s
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