XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #2,643,797

Block #2,643,797

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 5:57:16 AM Β· Difficulty 11.6936 Β· 4,201,856 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
198d5a176085e7bbd88fdd2049520ed754d43610e582874a9fd360365ad425fe
View on Chainz β†—

Difficulty

11.693650

Transactions

2

Size

425 B

Version

2

Bits

0bb19309

Nonce

933,264,681

Timestamp

5/2/2018, 5:57:16 AM

Confirmations

4,201,856

Merkle Root

569b124eb63018c620302a05d346ea46ef969155f6b447f6bf623e64a67ab72c
Transactions (2)
Coinbase74e13cb03e4148…ebe2cd16135052
1 in β†’ 1 out7.3100 XPM110 B
Adqah8zh…1WwoHJ9t
dff8365ee68c27…061cc8520a19c1
1 in β†’ 2 out238223.9468 XPM226 B
APoG3z2z…EvHdn2PVAd1nzX5a…3wgBTFzd
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.

2.061 Γ— 10⁹¹(92-digit number)
20612265840947887978…04957674825415720570
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
2.061 Γ— 10⁹¹(92-digit number)
20612265840947887978…04957674825415720569
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.122 Γ— 10⁹¹(92-digit number)
41224531681895775957…09915349650831441139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.244 Γ— 10⁹¹(92-digit number)
82449063363791551914…19830699301662882279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.648 Γ— 10⁹²(93-digit number)
16489812672758310382…39661398603325764559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.297 Γ— 10⁹²(93-digit number)
32979625345516620765…79322797206651529119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.595 Γ— 10⁹²(93-digit number)
65959250691033241531…58645594413303058239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.319 Γ— 10⁹³(94-digit number)
13191850138206648306…17291188826606116479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.638 Γ— 10⁹³(94-digit number)
26383700276413296612…34582377653212232959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.276 Γ— 10⁹³(94-digit number)
52767400552826593225…69164755306424465919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.055 Γ— 10⁹⁴(95-digit number)
10553480110565318645…38329510612848931839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.110 Γ— 10⁹⁴(95-digit number)
21106960221130637290…76659021225697863679
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 2643797

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 198d5a176085e7bbd88fdd2049520ed754d43610e582874a9fd360365ad425fe

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 #2,643,797 on Chainz β†—
Circulating Supply:58,009,672 XPMΒ·at block #6,845,652 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy