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Home/Chain Registry/Block #2,927,782

Block #2,927,782

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/18/2018, 2:22:44 AM Β· Difficulty 11.3675 Β· 3,915,278 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1be747bf3120e7c0b428cfebb562a048537adab8a973254ee35cd73c6faf3ae7
View on Chainz β†—

Difficulty

11.367547

Transactions

1

Size

200 B

Version

2

Bits

0b5e1794

Nonce

1,166,469,243

Timestamp

11/18/2018, 2:22:44 AM

Confirmations

3,915,278

Merkle Root

1f0184501f24988ef2d936847ec15f216ce9981df76cc23563208dd4fdf34fcb
Transactions (1)
Coinbase1f0184501f2498…208dd4fdf34fcb
1 in β†’ 1 out7.7300 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.

5.445 Γ— 10⁹⁢(97-digit number)
54457239770870170595…35757299588991869440
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
5.445 Γ— 10⁹⁢(97-digit number)
54457239770870170595…35757299588991869439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.089 Γ— 10⁹⁷(98-digit number)
10891447954174034119…71514599177983738879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.178 Γ— 10⁹⁷(98-digit number)
21782895908348068238…43029198355967477759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.356 Γ— 10⁹⁷(98-digit number)
43565791816696136476…86058396711934955519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.713 Γ— 10⁹⁷(98-digit number)
87131583633392272953…72116793423869911039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.742 Γ— 10⁹⁸(99-digit number)
17426316726678454590…44233586847739822079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.485 Γ— 10⁹⁸(99-digit number)
34852633453356909181…88467173695479644159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.970 Γ— 10⁹⁸(99-digit number)
69705266906713818362…76934347390959288319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.394 Γ— 10⁹⁹(100-digit number)
13941053381342763672…53868694781918576639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.788 Γ— 10⁹⁹(100-digit number)
27882106762685527345…07737389563837153279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.576 Γ— 10⁹⁹(100-digit number)
55764213525371054690…15474779127674306559
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 2927782

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 1be747bf3120e7c0b428cfebb562a048537adab8a973254ee35cd73c6faf3ae7

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 #2,927,782 on Chainz β†—
Circulating Supply:57,988,839 XPMΒ·at block #6,843,059 Β· updates every 60s
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