Block #463,287

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/28/2014, 12:25:26 AM · Difficulty 10.4166 · 6,348,462 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
155b4e54215b3ce62418c4db7cc312e357c148bee2364ba0b2021aa25203d3e7

Height

#463,287

Difficulty

10.416609

Transactions

2

Size

1.09 KB

Version

2

Bits

0a6aa6dd

Nonce

10,000,953

Timestamp

3/28/2014, 12:25:26 AM

Confirmations

6,348,462

Merkle Root

f8230380b31eab4b405295b1fbf62e5fb731c54f48fc917f33a283dc053f33f6
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.

3.490 × 10⁹⁵(96-digit number)
34906859321317221273…02595003432549664319
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
3.490 × 10⁹⁵(96-digit number)
34906859321317221273…02595003432549664319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.981 × 10⁹⁵(96-digit number)
69813718642634442546…05190006865099328639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.396 × 10⁹⁶(97-digit number)
13962743728526888509…10380013730198657279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.792 × 10⁹⁶(97-digit number)
27925487457053777018…20760027460397314559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.585 × 10⁹⁶(97-digit number)
55850974914107554037…41520054920794629119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.117 × 10⁹⁷(98-digit number)
11170194982821510807…83040109841589258239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.234 × 10⁹⁷(98-digit number)
22340389965643021615…66080219683178516479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.468 × 10⁹⁷(98-digit number)
44680779931286043230…32160439366357032959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.936 × 10⁹⁷(98-digit number)
89361559862572086460…64320878732714065919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.787 × 10⁹⁸(99-digit number)
17872311972514417292…28641757465428131839
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:57,738,102 XPM·at block #6,811,748 · updates every 60s
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