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Home/Chain Registry/Block #2,446,033

Block #2,446,033

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/28/2017, 1:23:10 PM Β· Difficulty 10.9415 Β· 4,390,518 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
21c7741cab5705ddd4698d91496b5ac0e591f035bcb62ef8e64f873a6ac11357
View on Chainz β†—

Difficulty

10.941479

Transactions

1

Size

200 B

Version

2

Bits

0af104bd

Nonce

928,264,434

Timestamp

12/28/2017, 1:23:10 PM

Confirmations

4,390,518

Merkle Root

3956874d673831951e423fbdc2d712974239a19a225d5190e100f3408942dea4
Transactions (1)
Coinbase3956874d673831…00f3408942dea4
1 in β†’ 1 out8.3400 XPM110 B
AGGzGc2Z…g8WZtyVL
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.

2.810 Γ— 10⁹⁴(95-digit number)
28108201325895530721…52376071730995250800
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
2.810 Γ— 10⁹⁴(95-digit number)
28108201325895530721…52376071730995250799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.621 Γ— 10⁹⁴(95-digit number)
56216402651791061443…04752143461990501599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.124 Γ— 10⁹⁡(96-digit number)
11243280530358212288…09504286923981003199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.248 Γ— 10⁹⁡(96-digit number)
22486561060716424577…19008573847962006399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.497 Γ— 10⁹⁡(96-digit number)
44973122121432849155…38017147695924012799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.994 Γ— 10⁹⁡(96-digit number)
89946244242865698310…76034295391848025599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.798 Γ— 10⁹⁢(97-digit number)
17989248848573139662…52068590783696051199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.597 Γ— 10⁹⁢(97-digit number)
35978497697146279324…04137181567392102399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.195 Γ— 10⁹⁢(97-digit number)
71956995394292558648…08274363134784204799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁷(98-digit number)
14391399078858511729…16548726269568409599
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
UncommonChain length 10
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 2446033

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 21c7741cab5705ddd4698d91496b5ac0e591f035bcb62ef8e64f873a6ac11357

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 #2,446,033 on Chainz β†—
Circulating Supply:57,936,673 XPMΒ·at block #6,836,550 Β· updates every 60s
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