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Home/Chain Registry/Block #2,634,886

Block #2,634,886

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/29/2018, 1:31:57 AM Β· Difficulty 11.2769 Β· 4,205,416 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8696cafaac95bde24ba181f4059426a365176e2031d87bd28a309e09392634ab
View on Chainz β†—

Difficulty

11.276931

Transactions

1

Size

200 B

Version

2

Bits

0b46e4ee

Nonce

1,965,994,983

Timestamp

4/29/2018, 1:31:57 AM

Confirmations

4,205,416

Merkle Root

ddfdbfb32b5c0632f8dc876e092ed1fcf8977d0e189e7df584529fdf02563bf4
Transactions (1)
Coinbaseddfdbfb32b5c06…529fdf02563bf4
1 in β†’ 1 out7.8500 XPM110 B
AcPEpnQQ…LysTjs6r
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.475 Γ— 10⁹³(94-digit number)
44757435769473170726…84912606453398905360
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.475 Γ— 10⁹³(94-digit number)
44757435769473170726…84912606453398905359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.951 Γ— 10⁹³(94-digit number)
89514871538946341452…69825212906797810719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.790 Γ— 10⁹⁴(95-digit number)
17902974307789268290…39650425813595621439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.580 Γ— 10⁹⁴(95-digit number)
35805948615578536581…79300851627191242879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.161 Γ— 10⁹⁴(95-digit number)
71611897231157073162…58601703254382485759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁡(96-digit number)
14322379446231414632…17203406508764971519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.864 Γ— 10⁹⁡(96-digit number)
28644758892462829264…34406813017529943039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.728 Γ— 10⁹⁡(96-digit number)
57289517784925658529…68813626035059886079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.145 Γ— 10⁹⁢(97-digit number)
11457903556985131705…37627252070119772159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.291 Γ— 10⁹⁢(97-digit number)
22915807113970263411…75254504140239544319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.583 Γ— 10⁹⁢(97-digit number)
45831614227940526823…50509008280479088639
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 2634886

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 8696cafaac95bde24ba181f4059426a365176e2031d87bd28a309e09392634ab

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,634,886 on Chainz β†—
Circulating Supply:57,966,733 XPMΒ·at block #6,840,301 Β· updates every 60s
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