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Home/Chain Registry/Block #3,503,191

Block #3,503,191

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2020, 1:25:22 AM Β· Difficulty 10.9307 Β· 3,324,045 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
f6cfd5e2fd5a89349a54518bb4e983ce6e0b5f4fcfd59c3cd2dcc24a4ef3d3a5
View on Chainz β†—

Difficulty

10.930704

Transactions

1

Size

199 B

Version

2

Bits

0aee4299

Nonce

290,781,034

Timestamp

1/7/2020, 1:25:22 AM

Confirmations

3,324,045

Merkle Root

9a50464c22ed27e64edac74cb14b97e1d3ce95974bad49b26ca32a40cd090232
Transactions (1)
Coinbase9a50464c22ed27…a32a40cd090232
1 in β†’ 1 out8.3600 XPM109 B
ASiq2qtK…VMhmk7yL
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.

3.467 Γ— 10⁹⁴(95-digit number)
34670546910870729150…21403624465239812800
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
3.467 Γ— 10⁹⁴(95-digit number)
34670546910870729150…21403624465239812799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.467 Γ— 10⁹⁴(95-digit number)
34670546910870729150…21403624465239812801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
6.934 Γ— 10⁹⁴(95-digit number)
69341093821741458300…42807248930479625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.934 Γ— 10⁹⁴(95-digit number)
69341093821741458300…42807248930479625601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.386 Γ— 10⁹⁡(96-digit number)
13868218764348291660…85614497860959251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.386 Γ— 10⁹⁡(96-digit number)
13868218764348291660…85614497860959251201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.773 Γ— 10⁹⁡(96-digit number)
27736437528696583320…71228995721918502399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.773 Γ— 10⁹⁡(96-digit number)
27736437528696583320…71228995721918502401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
5.547 Γ— 10⁹⁡(96-digit number)
55472875057393166640…42457991443837004799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.547 Γ— 10⁹⁡(96-digit number)
55472875057393166640…42457991443837004801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.109 Γ— 10⁹⁢(97-digit number)
11094575011478633328…84915982887674009599
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 3503191

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 f6cfd5e2fd5a89349a54518bb4e983ce6e0b5f4fcfd59c3cd2dcc24a4ef3d3a5

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 #3,503,191 on Chainz β†—
Circulating Supply:57,861,989 XPMΒ·at block #6,827,235 Β· updates every 60s
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