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Home/Chain Registry/Block #2,334,146

Block #2,334,146

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/12/2017, 6:55:16 PM Β· Difficulty 10.9209 Β· 4,507,952 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ffadf268c3f87e97a9c385ace1a855d8523dea2bd966dca390931c616d9af04c
View on Chainz β†—

Difficulty

10.920921

Transactions

2

Size

1.86 KB

Version

2

Bits

0aebc17e

Nonce

1,082,371,094

Timestamp

10/12/2017, 6:55:16 PM

Confirmations

4,507,952

Merkle Root

74b31faedda30696c7a392f70295a048478a68dcad1803e7d74bbe10217d0e68
Transactions (2)
Coinbasebec2c32bdd5a7a…5a3ec8b752051b
1 in β†’ 1 out8.3900 XPM110 B
AXqoq68n…y6dfh6ZP
fa9a6fbbb87bf2…011377015630ff
11 in β†’ 2 out744.2802 XPM1.67 KB
AakGpkRE…wGxg3jRBAbfHPQRP…cc1QCTYa
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.

4.899 Γ— 10⁹⁷(98-digit number)
48994839578076199962…32192670565158333440
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
4.899 Γ— 10⁹⁷(98-digit number)
48994839578076199962…32192670565158333439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.899 Γ— 10⁹⁷(98-digit number)
48994839578076199962…32192670565158333441
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
9.798 Γ— 10⁹⁷(98-digit number)
97989679156152399925…64385341130316666879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.798 Γ— 10⁹⁷(98-digit number)
97989679156152399925…64385341130316666881
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
1.959 Γ— 10⁹⁸(99-digit number)
19597935831230479985…28770682260633333759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.959 Γ— 10⁹⁸(99-digit number)
19597935831230479985…28770682260633333761
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
3.919 Γ— 10⁹⁸(99-digit number)
39195871662460959970…57541364521266667519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.919 Γ— 10⁹⁸(99-digit number)
39195871662460959970…57541364521266667521
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
7.839 Γ— 10⁹⁸(99-digit number)
78391743324921919940…15082729042533335039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.839 Γ— 10⁹⁸(99-digit number)
78391743324921919940…15082729042533335041
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
1.567 Γ— 10⁹⁹(100-digit number)
15678348664984383988…30165458085066670079
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 2334146

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 ffadf268c3f87e97a9c385ace1a855d8523dea2bd966dca390931c616d9af04c

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 #2,334,146 on Chainz β†—
Circulating Supply:57,981,170 XPMΒ·at block #6,842,097 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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