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Home/Chain Registry/Block #3,035,783

Block #3,035,783

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/2/2019, 4:31:17 PM Β· Difficulty 11.0107 Β· 3,806,690 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ec66361a6e1fd46e8f0d47ed84cac80160c173d4a8ab578cf68a81207674b6c4
View on Chainz β†—

Difficulty

11.010654

Transactions

1

Size

201 B

Version

2

Bits

0b02ba35

Nonce

1,420,309,899

Timestamp

2/2/2019, 4:31:17 PM

Confirmations

3,806,690

Merkle Root

674eab1f18f1254556b9d85fb27bcbb178253d5843e67cba52bb58e3e109e6c4
Transactions (1)
Coinbase674eab1f18f125…bb58e3e109e6c4
1 in β†’ 1 out8.2400 XPM110 B
AUMQRepm…tAfKmdW1
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.

5.460 Γ— 10⁹⁢(97-digit number)
54600133784719552421…20041898959117803520
Discovered Prime Numbers
p_k = 2^k Γ— 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
5.460 Γ— 10⁹⁢(97-digit number)
54600133784719552421…20041898959117803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.092 Γ— 10⁹⁷(98-digit number)
10920026756943910484…40083797918235607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.184 Γ— 10⁹⁷(98-digit number)
21840053513887820968…80167595836471214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.368 Γ— 10⁹⁷(98-digit number)
43680107027775641936…60335191672942428161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.736 Γ— 10⁹⁷(98-digit number)
87360214055551283873…20670383345884856321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.747 Γ— 10⁹⁸(99-digit number)
17472042811110256774…41340766691769712641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.494 Γ— 10⁹⁸(99-digit number)
34944085622220513549…82681533383539425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.988 Γ— 10⁹⁸(99-digit number)
69888171244441027098…65363066767078850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.397 Γ— 10⁹⁹(100-digit number)
13977634248888205419…30726133534157701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.795 Γ— 10⁹⁹(100-digit number)
27955268497776410839…61452267068315402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.591 Γ— 10⁹⁹(100-digit number)
55910536995552821679…22904534136630804481
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 3035783

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 ec66361a6e1fd46e8f0d47ed84cac80160c173d4a8ab578cf68a81207674b6c4

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 #3,035,783 on Chainz β†—
Circulating Supply:57,984,202 XPMΒ·at block #6,842,472 Β· updates every 60s
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