Block #2,623,499

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 4/21/2018, 10:23:49 AM · Difficulty 11.2170 · 4,218,685 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9313449dfc2e91afec8811e52024ef1e3d27a4850a1252ce5e2df09b208570e6

Height

#2,623,499

Difficulty

11.217033

Transactions

4

Size

1.19 KB

Version

2

Bits

0b378f7f

Nonce

200,626,899

Timestamp

4/21/2018, 10:23:49 AM

Confirmations

4,218,685

Merkle Root

0bf04b380f418816d00bc6fc004af86b82ad24b1585b59af5ac3c41829a2b6fb
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.

1.652 × 10⁹⁶(97-digit number)
16523888827006071338…61625022061444341759
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
1.652 × 10⁹⁶(97-digit number)
16523888827006071338…61625022061444341759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.304 × 10⁹⁶(97-digit number)
33047777654012142677…23250044122888683519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.609 × 10⁹⁶(97-digit number)
66095555308024285355…46500088245777367039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.321 × 10⁹⁷(98-digit number)
13219111061604857071…93000176491554734079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.643 × 10⁹⁷(98-digit number)
26438222123209714142…86000352983109468159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.287 × 10⁹⁷(98-digit number)
52876444246419428284…72000705966218936319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.057 × 10⁹⁸(99-digit number)
10575288849283885656…44001411932437872639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.115 × 10⁹⁸(99-digit number)
21150577698567771313…88002823864875745279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.230 × 10⁹⁸(99-digit number)
42301155397135542627…76005647729751490559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.460 × 10⁹⁸(99-digit number)
84602310794271085255…52011295459502981119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.692 × 10⁹⁹(100-digit number)
16920462158854217051…04022590919005962239
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,981,864 XPM·at block #6,842,183 · updates every 60s
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