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Block #234,304

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2013, 6:13:22 AM Β· Difficulty 9.9438 Β· 6,562,497 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1309dd5fd77ffde0c555f31a07ebf57c55a6173961cf2e57bb69c148ff241e4d
View on Chainz β†—

Height

#234,304

Difficulty

9.943826

Transactions

1

Size

208 B

Version

2

Bits

09f19e8d

Nonce

1,671,137

Timestamp

10/30/2013, 6:13:22 AM

Confirmations

6,562,497

Merkle Root

f70721ce04baeb76d7b8af718c4fdc4cc55fed78a3d140cf6f72250d9060b199
Transactions (1)
Coinbasef70721ce04baeb…72250d9060b199
1 in β†’ 1 out10.1000 XPM116 B
AcLBm5Z9…S683d7c3
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.

6.816 Γ— 10⁹⁹(100-digit number)
68162178711512849197…20926500073216267650
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
6.816 Γ— 10⁹⁹(100-digit number)
68162178711512849197…20926500073216267649
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.816 Γ— 10⁹⁹(100-digit number)
68162178711512849197…20926500073216267651
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
1.363 Γ— 10¹⁰⁰(101-digit number)
13632435742302569839…41853000146432535299
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.363 Γ— 10¹⁰⁰(101-digit number)
13632435742302569839…41853000146432535301
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
2.726 Γ— 10¹⁰⁰(101-digit number)
27264871484605139679…83706000292865070599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.726 Γ— 10¹⁰⁰(101-digit number)
27264871484605139679…83706000292865070601
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
5.452 Γ— 10¹⁰⁰(101-digit number)
54529742969210279358…67412000585730141199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.452 Γ— 10¹⁰⁰(101-digit number)
54529742969210279358…67412000585730141201
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
1.090 Γ— 10¹⁰¹(102-digit number)
10905948593842055871…34824001171460282399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 234304

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 1309dd5fd77ffde0c555f31a07ebf57c55a6173961cf2e57bb69c148ff241e4d

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 #234,304 on Chainz β†—
Circulating Supply:57,618,422 XPMΒ·at block #6,796,800 Β· updates every 60s
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