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Home/Chain Registry/Block #1,894,921

Block #1,894,921

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/15/2016, 7:04:29 AM Β· Difficulty 10.7477 Β· 4,929,640 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2cce70c8cdce2ad84604a7aad963b7c121619de286ef0a25f3ee4b0183083e48
View on Chainz β†—

Difficulty

10.747693

Transactions

1

Size

201 B

Version

2

Bits

0abf68d4

Nonce

1,794,438,757

Timestamp

12/15/2016, 7:04:29 AM

Confirmations

4,929,640

Merkle Root

525e5219d55793ffe5cf3efb0f1ea06ef2474d5c61623006a515c4066dac44d7
Transactions (1)
Coinbase525e5219d55793…15c4066dac44d7
1 in β†’ 1 out8.6400 XPM110 B
AR39UGAq…FioJzmzD
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.

1.604 Γ— 10⁹⁷(98-digit number)
16045553642453334393…30266151291854643200
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
1.604 Γ— 10⁹⁷(98-digit number)
16045553642453334393…30266151291854643199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.604 Γ— 10⁹⁷(98-digit number)
16045553642453334393…30266151291854643201
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
3.209 Γ— 10⁹⁷(98-digit number)
32091107284906668787…60532302583709286399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.209 Γ— 10⁹⁷(98-digit number)
32091107284906668787…60532302583709286401
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
6.418 Γ— 10⁹⁷(98-digit number)
64182214569813337575…21064605167418572799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.418 Γ— 10⁹⁷(98-digit number)
64182214569813337575…21064605167418572801
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
1.283 Γ— 10⁹⁸(99-digit number)
12836442913962667515…42129210334837145599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.283 Γ— 10⁹⁸(99-digit number)
12836442913962667515…42129210334837145601
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
2.567 Γ— 10⁹⁸(99-digit number)
25672885827925335030…84258420669674291199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.567 Γ— 10⁹⁸(99-digit number)
25672885827925335030…84258420669674291201
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 1894921

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 2cce70c8cdce2ad84604a7aad963b7c121619de286ef0a25f3ee4b0183083e48

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 #1,894,921 on Chainz β†—
Circulating Supply:57,840,552 XPMΒ·at block #6,824,560 Β· updates every 60s
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