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Home/Chain Registry/Block #2,130,983

Block #2,130,983

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2017, 6:59:15 PM Β· Difficulty 10.9103 Β· 4,706,078 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3078712ae7e6d2f55c64365cba847ff7d9a8d3793ef0c4ce4e82d6dd219d0906
View on Chainz β†—

Difficulty

10.910272

Transactions

2

Size

869 B

Version

2

Bits

0ae90792

Nonce

9,331,103

Timestamp

5/24/2017, 6:59:15 PM

Confirmations

4,706,078

Merkle Root

04f1de644989176af7b31b8999d2185d0cbd22e5b2022b53199a33e60304e8a0
Transactions (2)
Coinbase9b928ea789f5ba…6ee0db686b2c90
1 in β†’ 1 out8.4000 XPM109 B
AGtz9Fbb…3MrqJBXt
70608e0e7389d8…b722b2b3332534
4 in β†’ 2 out15.8225 XPM668 B
AZGHDMdT…dYpBoxtrAKGxoSP8…8oH3hVLd
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.

3.737 Γ— 10⁹⁸(99-digit number)
37371837010839721595…66477550482851430400
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
3.737 Γ— 10⁹⁸(99-digit number)
37371837010839721595…66477550482851430399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.737 Γ— 10⁹⁸(99-digit number)
37371837010839721595…66477550482851430401
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
7.474 Γ— 10⁹⁸(99-digit number)
74743674021679443191…32955100965702860799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.474 Γ— 10⁹⁸(99-digit number)
74743674021679443191…32955100965702860801
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
1.494 Γ— 10⁹⁹(100-digit number)
14948734804335888638…65910201931405721599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.494 Γ— 10⁹⁹(100-digit number)
14948734804335888638…65910201931405721601
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
2.989 Γ— 10⁹⁹(100-digit number)
29897469608671777276…31820403862811443199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.989 Γ— 10⁹⁹(100-digit number)
29897469608671777276…31820403862811443201
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
5.979 Γ— 10⁹⁹(100-digit number)
59794939217343554553…63640807725622886399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.979 Γ— 10⁹⁹(100-digit number)
59794939217343554553…63640807725622886401
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 2130983

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 3078712ae7e6d2f55c64365cba847ff7d9a8d3793ef0c4ce4e82d6dd219d0906

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 #2,130,983 on Chainz β†—
Circulating Supply:57,940,791 XPMΒ·at block #6,837,060 Β· updates every 60s
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