Block #2,471,628

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/13/2018, 8:48:44 PM · Difficulty 10.9622 · 4,369,018 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f5415d53b4a1f5b50cf16c088de4a921fbb4dce2967fb65924b200729ab814d7

Height

#2,471,628

Difficulty

10.962161

Transactions

5

Size

1.16 KB

Version

2

Bits

0af6502d

Nonce

1,934,986,624

Timestamp

1/13/2018, 8:48:44 PM

Confirmations

4,369,018

Merkle Root

6f57439372193a9f85945b5560440a4ca9f3b4e9896ff7124e1c29899685d732
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.

1.437 × 10⁹⁶(97-digit number)
14372756037847550135…06357665697093460479
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
1.437 × 10⁹⁶(97-digit number)
14372756037847550135…06357665697093460479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.874 × 10⁹⁶(97-digit number)
28745512075695100270…12715331394186920959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.749 × 10⁹⁶(97-digit number)
57491024151390200541…25430662788373841919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.149 × 10⁹⁷(98-digit number)
11498204830278040108…50861325576747683839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.299 × 10⁹⁷(98-digit number)
22996409660556080216…01722651153495367679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.599 × 10⁹⁷(98-digit number)
45992819321112160432…03445302306990735359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.198 × 10⁹⁷(98-digit number)
91985638642224320865…06890604613981470719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.839 × 10⁹⁸(99-digit number)
18397127728444864173…13781209227962941439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.679 × 10⁹⁸(99-digit number)
36794255456889728346…27562418455925882879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.358 × 10⁹⁸(99-digit number)
73588510913779456692…55124836911851765759
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:57,969,510 XPM·at block #6,840,645 · updates every 60s
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