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Home/Chain Registry/Block #2,954,659

Block #2,954,659

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/6/2018, 1:47:46 PM Β· Difficulty 11.4018 Β· 3,884,165 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9409aa251be59f3dea462c4e0908cb0683a7cc219b39857390070fefde5b59fc
View on Chainz β†—

Difficulty

11.401794

Transactions

1

Size

201 B

Version

2

Bits

0b66dbf9

Nonce

131,343,952

Timestamp

12/6/2018, 1:47:46 PM

Confirmations

3,884,165

Merkle Root

5b566a055edc63a2ca968db704bd7bbae2fadc00a15922072deb72640df95413
Transactions (1)
Coinbase5b566a055edc63…eb72640df95413
1 in β†’ 1 out7.6800 XPM110 B
AUhjokok…k5m93PZR
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.

2.326 Γ— 10⁹⁷(98-digit number)
23267366967105652752…01188176480782336000
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
2.326 Γ— 10⁹⁷(98-digit number)
23267366967105652752…01188176480782335999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.326 Γ— 10⁹⁷(98-digit number)
23267366967105652752…01188176480782336001
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
4.653 Γ— 10⁹⁷(98-digit number)
46534733934211305504…02376352961564671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.653 Γ— 10⁹⁷(98-digit number)
46534733934211305504…02376352961564672001
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
9.306 Γ— 10⁹⁷(98-digit number)
93069467868422611009…04752705923129343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.306 Γ— 10⁹⁷(98-digit number)
93069467868422611009…04752705923129344001
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
1.861 Γ— 10⁹⁸(99-digit number)
18613893573684522201…09505411846258687999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.861 Γ— 10⁹⁸(99-digit number)
18613893573684522201…09505411846258688001
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
3.722 Γ— 10⁹⁸(99-digit number)
37227787147369044403…19010823692517375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.722 Γ— 10⁹⁸(99-digit number)
37227787147369044403…19010823692517376001
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
7.445 Γ— 10⁹⁸(99-digit number)
74455574294738088807…38021647385034751999
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 2954659

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 9409aa251be59f3dea462c4e0908cb0683a7cc219b39857390070fefde5b59fc

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 #2,954,659 on Chainz β†—
Circulating Supply:57,954,858 XPMΒ·at block #6,838,823 Β· updates every 60s
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