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Home/Chain Registry/Block #2,096,558

Block #2,096,558

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2017, 1:56:09 AM Β· Difficulty 10.8723 Β· 4,740,179 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
869052a5985535899b2d90bf76ec423c850bf65e4a0bbf7e608c0cfe588894f5
View on Chainz β†—

Difficulty

10.872342

Transactions

1

Size

201 B

Version

2

Bits

0adf51c9

Nonce

1,219,803,383

Timestamp

5/2/2017, 1:56:09 AM

Confirmations

4,740,179

Merkle Root

f9a47d362789f037e6b1d6c012e10d831e070bcb82b7d44e67271a5d0cbf47f0
Transactions (1)
Coinbasef9a47d362789f0…271a5d0cbf47f0
1 in β†’ 1 out8.4500 XPM110 B
AFtCkp2n…Ba58Rq8c
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.

3.667 Γ— 10⁹⁢(97-digit number)
36677106688558055336…29357709952757297920
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
3.667 Γ— 10⁹⁢(97-digit number)
36677106688558055336…29357709952757297919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.667 Γ— 10⁹⁢(97-digit number)
36677106688558055336…29357709952757297921
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
7.335 Γ— 10⁹⁢(97-digit number)
73354213377116110673…58715419905514595839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.335 Γ— 10⁹⁢(97-digit number)
73354213377116110673…58715419905514595841
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
1.467 Γ— 10⁹⁷(98-digit number)
14670842675423222134…17430839811029191679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.467 Γ— 10⁹⁷(98-digit number)
14670842675423222134…17430839811029191681
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
2.934 Γ— 10⁹⁷(98-digit number)
29341685350846444269…34861679622058383359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.934 Γ— 10⁹⁷(98-digit number)
29341685350846444269…34861679622058383361
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
5.868 Γ— 10⁹⁷(98-digit number)
58683370701692888538…69723359244116766719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.868 Γ— 10⁹⁷(98-digit number)
58683370701692888538…69723359244116766721
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 2096558

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 869052a5985535899b2d90bf76ec423c850bf65e4a0bbf7e608c0cfe588894f5

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 #2,096,558 on Chainz β†—
Circulating Supply:57,938,179 XPMΒ·at block #6,836,736 Β· updates every 60s
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