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Block #2,652,641

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/7/2018, 6:32:37 PM Β· Difficulty 11.7435 Β· 4,179,763 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e24072b1ba9416cddf116c1c7d0dbc6e82c0907340c3bea96f3416a3d1b30593
View on Chainz β†—

Difficulty

11.743543

Transactions

2

Size

873 B

Version

2

Bits

0bbe58dc

Nonce

427,943,568

Timestamp

5/7/2018, 6:32:37 PM

Confirmations

4,179,763

Merkle Root

1f3ec28ae6812a55a68b274e7f64baaa403e9be36fc2fdad378deeaec402f2da
Transactions (2)
Coinbase09183e583d9c6a…d155cdea36edf3
1 in β†’ 1 out7.2600 XPM110 B
AL8gd23g…3C6Herfc
cf3f703f8eda37…4a1bd83fac81ab
4 in β†’ 2 out55.0102 XPM672 B
AcV3mqbY…9hsdR3LtAdxhHnzE…xfUM6A2f
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.

2.416 Γ— 10⁹⁢(97-digit number)
24164821658712808008…93415599572484935680
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
2.416 Γ— 10⁹⁢(97-digit number)
24164821658712808008…93415599572484935679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.416 Γ— 10⁹⁢(97-digit number)
24164821658712808008…93415599572484935681
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
4.832 Γ— 10⁹⁢(97-digit number)
48329643317425616017…86831199144969871359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.832 Γ— 10⁹⁢(97-digit number)
48329643317425616017…86831199144969871361
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
9.665 Γ— 10⁹⁢(97-digit number)
96659286634851232034…73662398289939742719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.665 Γ— 10⁹⁢(97-digit number)
96659286634851232034…73662398289939742721
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
1.933 Γ— 10⁹⁷(98-digit number)
19331857326970246406…47324796579879485439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.933 Γ— 10⁹⁷(98-digit number)
19331857326970246406…47324796579879485441
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
3.866 Γ— 10⁹⁷(98-digit number)
38663714653940492813…94649593159758970879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.866 Γ— 10⁹⁷(98-digit number)
38663714653940492813…94649593159758970881
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
7.732 Γ— 10⁹⁷(98-digit number)
77327429307880985627…89299186319517941759
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 2652641

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 e24072b1ba9416cddf116c1c7d0dbc6e82c0907340c3bea96f3416a3d1b30593

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 #2,652,641 on Chainz β†—
Circulating Supply:57,903,376 XPMΒ·at block #6,832,403 Β· updates every 60s
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