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Home/Chain Registry/Block #2,831,649

Block #2,831,649

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/9/2018, 11:38:37 AM Β· Difficulty 11.7175 Β· 4,006,676 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d6337781cdf12e275d62d8afe0deb4f814614e0a34f7268a3f43089a1da3f21f
View on Chainz β†—

Difficulty

11.717549

Transactions

1

Size

200 B

Version

2

Bits

0bb7b144

Nonce

190,834,738

Timestamp

9/9/2018, 11:38:37 AM

Confirmations

4,006,676

Merkle Root

15638537dc764e4e901794da89fca1c4a16e8868418588454e59117986537958
Transactions (1)
Coinbase15638537dc764e…59117986537958
1 in β†’ 1 out7.2700 XPM110 B
AHuqWxwp…3UFqGKpc
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.

5.867 Γ— 10⁹⁡(96-digit number)
58671250698356851597…92285216212280980480
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
5.867 Γ— 10⁹⁡(96-digit number)
58671250698356851597…92285216212280980479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.867 Γ— 10⁹⁡(96-digit number)
58671250698356851597…92285216212280980481
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
1.173 Γ— 10⁹⁢(97-digit number)
11734250139671370319…84570432424561960959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.173 Γ— 10⁹⁢(97-digit number)
11734250139671370319…84570432424561960961
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
2.346 Γ— 10⁹⁢(97-digit number)
23468500279342740638…69140864849123921919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.346 Γ— 10⁹⁢(97-digit number)
23468500279342740638…69140864849123921921
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
4.693 Γ— 10⁹⁢(97-digit number)
46937000558685481277…38281729698247843839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.693 Γ— 10⁹⁢(97-digit number)
46937000558685481277…38281729698247843841
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
9.387 Γ— 10⁹⁢(97-digit number)
93874001117370962555…76563459396495687679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.387 Γ— 10⁹⁢(97-digit number)
93874001117370962555…76563459396495687681
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
1.877 Γ— 10⁹⁷(98-digit number)
18774800223474192511…53126918792991375359
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 2831649

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 d6337781cdf12e275d62d8afe0deb4f814614e0a34f7268a3f43089a1da3f21f

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 #2,831,649 on Chainz β†—
Circulating Supply:57,950,877 XPMΒ·at block #6,838,324 Β· updates every 60s
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