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Home/Chain Registry/Block #3,054,129

Block #3,054,129

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 2/15/2019, 4:12:37 PM Β· Difficulty 11.0017 Β· 3,790,776 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9176fed5a3dee9c2e4c3937abb291ddea4906fbe9b0f0d29dca1c5e81bb43f5b
View on Chainz β†—

Difficulty

11.001670

Transactions

1

Size

199 B

Version

2

Bits

0b006d73

Nonce

59,204,274

Timestamp

2/15/2019, 4:12:37 PM

Confirmations

3,790,776

Merkle Root

1ea506f4729b21ae1a765c862ccaf432afe61633d1a8ae6bb532a2bf8b03ffc5
Transactions (1)
Coinbase1ea506f4729b21…32a2bf8b03ffc5
1 in β†’ 1 out8.2500 XPM109 B
AbXwmGxD…4XXYP765
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.

5.828 Γ— 10⁹⁴(95-digit number)
58282464568440779887…91524530706245312480
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
5.828 Γ— 10⁹⁴(95-digit number)
58282464568440779887…91524530706245312479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.165 Γ— 10⁹⁡(96-digit number)
11656492913688155977…83049061412490624959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.331 Γ— 10⁹⁡(96-digit number)
23312985827376311954…66098122824981249919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.662 Γ— 10⁹⁡(96-digit number)
46625971654752623909…32196245649962499839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.325 Γ— 10⁹⁡(96-digit number)
93251943309505247819…64392491299924999679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.865 Γ— 10⁹⁢(97-digit number)
18650388661901049563…28784982599849999359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.730 Γ— 10⁹⁢(97-digit number)
37300777323802099127…57569965199699998719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.460 Γ— 10⁹⁢(97-digit number)
74601554647604198255…15139930399399997439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.492 Γ— 10⁹⁷(98-digit number)
14920310929520839651…30279860798799994879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.984 Γ— 10⁹⁷(98-digit number)
29840621859041679302…60559721597599989759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.968 Γ— 10⁹⁷(98-digit number)
59681243718083358604…21119443195199979519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁸(99-digit number)
11936248743616671720…42238886390399959039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12
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 3054129

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 9176fed5a3dee9c2e4c3937abb291ddea4906fbe9b0f0d29dca1c5e81bb43f5b

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 #3,054,129 on Chainz β†—
Circulating Supply:58,003,654 XPMΒ·at block #6,844,904 Β· updates every 60s
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