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Home/Chain Registry/Block #2,176,966

Block #2,176,966

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 7:23:38 AM Β· Difficulty 10.9214 Β· 4,662,902 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e13529318d22c6639f41564c8a42d7bc086924d9daf784f2457f442091c4e81
View on Chainz β†—

Difficulty

10.921438

Transactions

1

Size

199 B

Version

2

Bits

0aebe355

Nonce

1,643,661,089

Timestamp

6/25/2017, 7:23:38 AM

Confirmations

4,662,902

Merkle Root

2682750028697982fa4e9533cf1b877ce74eff78ad8a602fed37785c7e8ee940
Transactions (1)
Coinbase26827500286979…37785c7e8ee940
1 in β†’ 1 out8.3700 XPM109 B
AYK3vMqf…zPbEEZ7u
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.

2.530 Γ— 10⁹⁡(96-digit number)
25306454447765389401…79790734021420398080
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
2.530 Γ— 10⁹⁡(96-digit number)
25306454447765389401…79790734021420398079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.530 Γ— 10⁹⁡(96-digit number)
25306454447765389401…79790734021420398081
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
5.061 Γ— 10⁹⁡(96-digit number)
50612908895530778803…59581468042840796159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.061 Γ— 10⁹⁡(96-digit number)
50612908895530778803…59581468042840796161
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
1.012 Γ— 10⁹⁢(97-digit number)
10122581779106155760…19162936085681592319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.012 Γ— 10⁹⁢(97-digit number)
10122581779106155760…19162936085681592321
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
2.024 Γ— 10⁹⁢(97-digit number)
20245163558212311521…38325872171363184639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.024 Γ— 10⁹⁢(97-digit number)
20245163558212311521…38325872171363184641
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
4.049 Γ— 10⁹⁢(97-digit number)
40490327116424623042…76651744342726369279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.049 Γ— 10⁹⁢(97-digit number)
40490327116424623042…76651744342726369281
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 2176966

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 3e13529318d22c6639f41564c8a42d7bc086924d9daf784f2457f442091c4e81

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 #2,176,966 on Chainz β†—
Circulating Supply:57,963,244 XPMΒ·at block #6,839,867 Β· updates every 60s
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