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Home/Chain Registry/Block #2,147,139

Block #2,147,139

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/5/2017, 3:45:32 PM Β· Difficulty 10.8926 Β· 4,695,294 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3e070ea8372bcd4c42dec60e4880ee694039aed2fdb80ef27a7fb4467f3dc04
View on Chainz β†—

Difficulty

10.892600

Transactions

1

Size

199 B

Version

2

Bits

0ae4816b

Nonce

1,990,130,788

Timestamp

6/5/2017, 3:45:32 PM

Confirmations

4,695,294

Merkle Root

3db88fd1c3558efdb4ca1aa46184896abd4a2d65aec9b8de25ff55e4b129319b
Transactions (1)
Coinbase3db88fd1c3558e…ff55e4b129319b
1 in β†’ 1 out8.4100 XPM109 B
ANGcJkZb…XMQyg4P6
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.

3.185 Γ— 10⁹⁡(96-digit number)
31853781198108651571…08184806845111851520
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
3.185 Γ— 10⁹⁡(96-digit number)
31853781198108651571…08184806845111851519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.185 Γ— 10⁹⁡(96-digit number)
31853781198108651571…08184806845111851521
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
6.370 Γ— 10⁹⁡(96-digit number)
63707562396217303143…16369613690223703039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.370 Γ— 10⁹⁡(96-digit number)
63707562396217303143…16369613690223703041
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
1.274 Γ— 10⁹⁢(97-digit number)
12741512479243460628…32739227380447406079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.274 Γ— 10⁹⁢(97-digit number)
12741512479243460628…32739227380447406081
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
2.548 Γ— 10⁹⁢(97-digit number)
25483024958486921257…65478454760894812159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.548 Γ— 10⁹⁢(97-digit number)
25483024958486921257…65478454760894812161
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
5.096 Γ— 10⁹⁢(97-digit number)
50966049916973842514…30956909521789624319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.096 Γ— 10⁹⁢(97-digit number)
50966049916973842514…30956909521789624321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2147139

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 d3e070ea8372bcd4c42dec60e4880ee694039aed2fdb80ef27a7fb4467f3dc04

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 #2,147,139 on Chainz β†—
Circulating Supply:57,983,879 XPMΒ·at block #6,842,432 Β· updates every 60s
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