Block #484,535

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/10/2014, 2:34:57 PM · Difficulty 10.5893 · 6,324,477 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86748a507fb5ed5a3452a4a09e384156aa17437d4da1bf060e817416c82b5e4a

Height

#484,535

Difficulty

10.589344

Transactions

2

Size

690 B

Version

2

Bits

0a96df39

Nonce

13,869

Timestamp

4/10/2014, 2:34:57 PM

Confirmations

6,324,477

Merkle Root

52aee177304e17007e131e830af2e433c79f9daeb291701b1b67527273a30456
Transactions (2)
1 in → 1 out8.9129 XPM110 B
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.

3.268 × 10¹⁰²(103-digit number)
32685370471755140294…91765238806707103199
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
3.268 × 10¹⁰²(103-digit number)
32685370471755140294…91765238806707103199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.537 × 10¹⁰²(103-digit number)
65370740943510280588…83530477613414206399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.307 × 10¹⁰³(104-digit number)
13074148188702056117…67060955226828412799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.614 × 10¹⁰³(104-digit number)
26148296377404112235…34121910453656825599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.229 × 10¹⁰³(104-digit number)
52296592754808224470…68243820907313651199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.045 × 10¹⁰⁴(105-digit number)
10459318550961644894…36487641814627302399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.091 × 10¹⁰⁴(105-digit number)
20918637101923289788…72975283629254604799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.183 × 10¹⁰⁴(105-digit number)
41837274203846579576…45950567258509209599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.367 × 10¹⁰⁴(105-digit number)
83674548407693159153…91901134517018419199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.673 × 10¹⁰⁵(106-digit number)
16734909681538631830…83802269034036838399
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:57,716,157 XPM·at block #6,809,011 · updates every 60s
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