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Home/Chain Registry/Block #3,364,734

Block #3,364,734

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2019, 7:54:24 AM Β· Difficulty 10.9954 Β· 3,462,410 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
af7d2b91e5355e343feca78b7391927d7d1cfbf8f3403bf3805c2f64829fd0cb
View on Chainz β†—

Difficulty

10.995449

Transactions

3

Size

698 B

Version

2

Bits

0afed5c0

Nonce

768,407,621

Timestamp

9/22/2019, 7:54:24 AM

Confirmations

3,462,410

Merkle Root

6083376b874f3eb805cd32a09c34437d60bd78bc83005b3511dea2da0a22d4c0
Transactions (3)
Coinbasea2e21bfacda4db…8c4e4194720291
1 in β†’ 1 out8.2800 XPM110 B
ASiq2qtK…VMhmk7yL
6c13a0885e11f6…5667e14d509f62
2 in β†’ 2 out16.5100 XPM305 B
AdGFnV3a…o6n2zX3xASiq2qtK…VMhmk7yL
ac5b889f785927…e311458745c76b
1 in β†’ 2 out8.2500 XPM193 B
ASiq2qtK…VMhmk7yLAP28h7vP…j3iRNVg2
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.

6.027 Γ— 10⁹⁴(95-digit number)
60272651315183787425…18917037776103190400
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
6.027 Γ— 10⁹⁴(95-digit number)
60272651315183787425…18917037776103190401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.205 Γ— 10⁹⁡(96-digit number)
12054530263036757485…37834075552206380801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.410 Γ— 10⁹⁡(96-digit number)
24109060526073514970…75668151104412761601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.821 Γ— 10⁹⁡(96-digit number)
48218121052147029940…51336302208825523201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.643 Γ— 10⁹⁡(96-digit number)
96436242104294059881…02672604417651046401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.928 Γ— 10⁹⁢(97-digit number)
19287248420858811976…05345208835302092801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.857 Γ— 10⁹⁢(97-digit number)
38574496841717623952…10690417670604185601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.714 Γ— 10⁹⁢(97-digit number)
77148993683435247904…21380835341208371201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.542 Γ— 10⁹⁷(98-digit number)
15429798736687049580…42761670682416742401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.085 Γ— 10⁹⁷(98-digit number)
30859597473374099161…85523341364833484801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.171 Γ— 10⁹⁷(98-digit number)
61719194946748198323…71046682729666969601
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 3364734

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 af7d2b91e5355e343feca78b7391927d7d1cfbf8f3403bf3805c2f64829fd0cb

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 #3,364,734 on Chainz β†—
Circulating Supply:57,861,334 XPMΒ·at block #6,827,143 Β· updates every 60s
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