Block #485,959

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/11/2014, 8:45:09 AM · Difficulty 10.6162 · 6,328,509 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fbac21ffbdb30320a345f721ea528c322c591e76a4ddee57b7d181e288dea136

Height

#485,959

Difficulty

10.616229

Transactions

1

Size

901 B

Version

2

Bits

0a9dc12c

Nonce

11,937

Timestamp

4/11/2014, 8:45:09 AM

Confirmations

6,328,509

Merkle Root

1a047cf6d76910c6216f60bb0b3315603452b35489711f8818d187571c0de573
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.

7.290 × 10⁹⁴(95-digit number)
72909091108642145365…40932547916664181999
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
7.290 × 10⁹⁴(95-digit number)
72909091108642145365…40932547916664181999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.458 × 10⁹⁵(96-digit number)
14581818221728429073…81865095833328363999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.916 × 10⁹⁵(96-digit number)
29163636443456858146…63730191666656727999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.832 × 10⁹⁵(96-digit number)
58327272886913716292…27460383333313455999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.166 × 10⁹⁶(97-digit number)
11665454577382743258…54920766666626911999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.333 × 10⁹⁶(97-digit number)
23330909154765486516…09841533333253823999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.666 × 10⁹⁶(97-digit number)
46661818309530973033…19683066666507647999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.332 × 10⁹⁶(97-digit number)
93323636619061946067…39366133333015295999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.866 × 10⁹⁷(98-digit number)
18664727323812389213…78732266666030591999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.732 × 10⁹⁷(98-digit number)
37329454647624778427…57464533332061183999
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:57,759,817 XPM·at block #6,814,467 · updates every 60s
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