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Home/Chain Registry/Block #2,925,348

Block #2,925,348

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2018, 11:27:02 AM Β· Difficulty 11.3550 Β· 3,917,705 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
50158dee67abf2917567206bbfae64669c6fc8a04a5614bfad1e0b6504a11235
View on Chainz β†—

Difficulty

11.354979

Transactions

1

Size

200 B

Version

2

Bits

0b5adfea

Nonce

692,368,295

Timestamp

11/16/2018, 11:27:02 AM

Confirmations

3,917,705

Merkle Root

5f8b7dbc043b01fe0219c0c763c49102cd4b5798b9699e1f122efecd3a7d14c1
Transactions (1)
Coinbase5f8b7dbc043b01…2efecd3a7d14c1
1 in β†’ 1 out7.7400 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.

1.044 Γ— 10⁹⁢(97-digit number)
10444508940080066568…17997246423714775040
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
1.044 Γ— 10⁹⁢(97-digit number)
10444508940080066568…17997246423714775039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.088 Γ— 10⁹⁢(97-digit number)
20889017880160133137…35994492847429550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.177 Γ— 10⁹⁢(97-digit number)
41778035760320266274…71988985694859100159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.355 Γ— 10⁹⁢(97-digit number)
83556071520640532549…43977971389718200319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.671 Γ— 10⁹⁷(98-digit number)
16711214304128106509…87955942779436400639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.342 Γ— 10⁹⁷(98-digit number)
33422428608256213019…75911885558872801279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.684 Γ— 10⁹⁷(98-digit number)
66844857216512426039…51823771117745602559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.336 Γ— 10⁹⁸(99-digit number)
13368971443302485207…03647542235491205119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.673 Γ— 10⁹⁸(99-digit number)
26737942886604970415…07295084470982410239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.347 Γ— 10⁹⁸(99-digit number)
53475885773209940831…14590168941964820479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁹(100-digit number)
10695177154641988166…29180337883929640959
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 2925348

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 50158dee67abf2917567206bbfae64669c6fc8a04a5614bfad1e0b6504a11235

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 #2,925,348 on Chainz β†—
Circulating Supply:57,988,782 XPMΒ·at block #6,843,052 Β· updates every 60s
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