Block #373,908

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 3:25:15 PM · Difficulty 10.4263 · 6,451,222 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a1ea3826a36d1164c29854be1e7315a5fcc37565ae0a634034581ec9ecb44a5d

Height

#373,908

Difficulty

10.426297

Transactions

3

Size

1.38 KB

Version

2

Bits

0a6d21cf

Nonce

1,832,985

Timestamp

1/24/2014, 3:25:15 PM

Confirmations

6,451,222

Merkle Root

1aaa160c80f66b5dc758d57e133b81af37ea44e579bf995ad6a67a764b0b8015
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.

1.154 × 10⁹⁶(97-digit number)
11547276041855419448…87863511769098493119
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
1.154 × 10⁹⁶(97-digit number)
11547276041855419448…87863511769098493119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.309 × 10⁹⁶(97-digit number)
23094552083710838896…75727023538196986239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.618 × 10⁹⁶(97-digit number)
46189104167421677793…51454047076393972479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.237 × 10⁹⁶(97-digit number)
92378208334843355587…02908094152787944959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.847 × 10⁹⁷(98-digit number)
18475641666968671117…05816188305575889919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.695 × 10⁹⁷(98-digit number)
36951283333937342234…11632376611151779839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.390 × 10⁹⁷(98-digit number)
73902566667874684469…23264753222303559679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.478 × 10⁹⁸(99-digit number)
14780513333574936893…46529506444607119359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.956 × 10⁹⁸(99-digit number)
29561026667149873787…93059012889214238719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.912 × 10⁹⁸(99-digit number)
59122053334299747575…86118025778428477439
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:57,845,124 XPM·at block #6,825,129 · updates every 60s
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