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Block #3,480,514

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/18/2019, 2:16:46 AM Β· Difficulty 10.9788 Β· 3,361,790 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
80db5f7e4e0acace25be53d24b5356a82e4ac5efe39d8db07094cbda4c0e1af7
View on Chainz β†—

Difficulty

10.978801

Transactions

1

Size

200 B

Version

2

Bits

0afa92ae

Nonce

654,255,300

Timestamp

12/18/2019, 2:16:46 AM

Confirmations

3,361,790

Merkle Root

fb0c9012d1fb1846a636f368e379942b506bde9169d7a5ef437d004da71c2ea9
Transactions (1)
Coinbasefb0c9012d1fb18…7d004da71c2ea9
1 in β†’ 1 out8.2800 XPM110 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.

1.981 Γ— 10⁹⁡(96-digit number)
19814282358897999650…41902667839551874960
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
1.981 Γ— 10⁹⁡(96-digit number)
19814282358897999650…41902667839551874959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.981 Γ— 10⁹⁡(96-digit number)
19814282358897999650…41902667839551874961
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
3.962 Γ— 10⁹⁡(96-digit number)
39628564717795999301…83805335679103749919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.962 Γ— 10⁹⁡(96-digit number)
39628564717795999301…83805335679103749921
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
7.925 Γ— 10⁹⁡(96-digit number)
79257129435591998602…67610671358207499839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.925 Γ— 10⁹⁡(96-digit number)
79257129435591998602…67610671358207499841
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
1.585 Γ— 10⁹⁢(97-digit number)
15851425887118399720…35221342716414999679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.585 Γ— 10⁹⁢(97-digit number)
15851425887118399720…35221342716414999681
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
3.170 Γ— 10⁹⁢(97-digit number)
31702851774236799441…70442685432829999359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.170 Γ— 10⁹⁢(97-digit number)
31702851774236799441…70442685432829999361
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
6.340 Γ— 10⁹⁢(97-digit number)
63405703548473598882…40885370865659998719
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 3480514

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 80db5f7e4e0acace25be53d24b5356a82e4ac5efe39d8db07094cbda4c0e1af7

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 #3,480,514 on Chainz β†—
Circulating Supply:57,982,837 XPMΒ·at block #6,842,303 Β· updates every 60s
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