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Home/Chain Registry/Block #2,648,892

Block #2,648,892

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 5/4/2018, 8:34:53 PM Β· Difficulty 11.7653 Β· 4,185,023 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c0a2681bc3c536b669c3b0454534151906f23a0e714feb8a423730e002946e55
View on Chainz β†—

Difficulty

11.765322

Transactions

2

Size

1017 B

Version

2

Bits

0bc3ec29

Nonce

1,711,831,923

Timestamp

5/4/2018, 8:34:53 PM

Confirmations

4,185,023

Merkle Root

8e1c90f00e4dae3c9029b12d46ecf5cd8efd3bbdbbc6014e15488e5dfa27f31c
Transactions (2)
Coinbased8e375240aef29…5dea50bab09779
1 in β†’ 1 out7.2200 XPM110 B
APhKkvsw…hxSyjytT
a1636bf6e5def6…172b7f2f6bb244
5 in β†’ 2 out3000.0113 XPM817 B
AWNHm6iZ…Uoz87gKoAH3A2GJU…NLYdkucb
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.

2.379 Γ— 10⁹⁴(95-digit number)
23798581770738441445…79750701956778916480
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
2.379 Γ— 10⁹⁴(95-digit number)
23798581770738441445…79750701956778916479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.759 Γ— 10⁹⁴(95-digit number)
47597163541476882890…59501403913557832959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.519 Γ— 10⁹⁴(95-digit number)
95194327082953765781…19002807827115665919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.903 Γ— 10⁹⁡(96-digit number)
19038865416590753156…38005615654231331839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.807 Γ— 10⁹⁡(96-digit number)
38077730833181506312…76011231308462663679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.615 Γ— 10⁹⁡(96-digit number)
76155461666363012625…52022462616925327359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.523 Γ— 10⁹⁢(97-digit number)
15231092333272602525…04044925233850654719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.046 Γ— 10⁹⁢(97-digit number)
30462184666545205050…08089850467701309439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.092 Γ— 10⁹⁢(97-digit number)
60924369333090410100…16179700935402618879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.218 Γ— 10⁹⁷(98-digit number)
12184873866618082020…32359401870805237759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.436 Γ— 10⁹⁷(98-digit number)
24369747733236164040…64718803741610475519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
4.873 Γ— 10⁹⁷(98-digit number)
48739495466472328080…29437607483220951039
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 2648892

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 c0a2681bc3c536b669c3b0454534151906f23a0e714feb8a423730e002946e55

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 #2,648,892 on Chainz β†—
Circulating Supply:57,915,546 XPMΒ·at block #6,833,914 Β· updates every 60s
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