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Home/Chain Registry/Block #2,766,152

Block #2,766,152

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/26/2018, 1:04:50 PM Β· Difficulty 11.6679 Β· 4,076,286 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f7d2db31cf372bd8e3aac63ed1c5ebaa10766729fbd550d4d0133286916d8fa0
View on Chainz β†—

Difficulty

11.667874

Transactions

1

Size

200 B

Version

2

Bits

0baaf9cb

Nonce

1,303,880

Timestamp

7/26/2018, 1:04:50 PM

Confirmations

4,076,286

Merkle Root

8c169d6fb669c76f891478913d611454979b897060bd90562aeb37579abe5fe5
Transactions (1)
Coinbase8c169d6fb669c7…eb37579abe5fe5
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
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.

9.642 Γ— 10⁹³(94-digit number)
96422452844652735897…52762134670813856320
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
9.642 Γ— 10⁹³(94-digit number)
96422452844652735897…52762134670813856321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.928 Γ— 10⁹⁴(95-digit number)
19284490568930547179…05524269341627712641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.856 Γ— 10⁹⁴(95-digit number)
38568981137861094359…11048538683255425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.713 Γ— 10⁹⁴(95-digit number)
77137962275722188718…22097077366510850561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.542 Γ— 10⁹⁡(96-digit number)
15427592455144437743…44194154733021701121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.085 Γ— 10⁹⁡(96-digit number)
30855184910288875487…88388309466043402241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.171 Γ— 10⁹⁡(96-digit number)
61710369820577750974…76776618932086804481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.234 Γ— 10⁹⁢(97-digit number)
12342073964115550194…53553237864173608961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.468 Γ— 10⁹⁢(97-digit number)
24684147928231100389…07106475728347217921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.936 Γ— 10⁹⁢(97-digit number)
49368295856462200779…14212951456694435841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.873 Γ— 10⁹⁢(97-digit number)
98736591712924401559…28425902913388871681
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 2766152

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 f7d2db31cf372bd8e3aac63ed1c5ebaa10766729fbd550d4d0133286916d8fa0

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 #2,766,152 on Chainz β†—
Circulating Supply:57,983,920 XPMΒ·at block #6,842,437 Β· updates every 60s
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