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Block #343,996

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/5/2014, 12:46:15 AM Β· Difficulty 10.1883 Β· 6,480,718 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5bc5c3faf53104e414a770b657b41e93d5dfff28a6a7cbe5827a989d0632021c
View on Chainz β†—

Height

#343,996

Difficulty

10.188338

Transactions

1

Size

230 B

Version

2

Bits

0a3036e5

Nonce

10,846

Timestamp

1/5/2014, 12:46:15 AM

Confirmations

6,480,718

Merkle Root

45078a7fe1b3d65ade6bda7af918c342184e59cdfdb0a67153be6c859cda045b
Transactions (1)
Coinbase45078a7fe1b3d6…be6c859cda045b
1 in β†’ 2 out9.6200 XPM136 B
AQ9VkUy6…TuxTAEugARa2UGtg…VkVUHq51
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.

1.663 Γ— 10¹⁰⁴(105-digit number)
16630107063437543990…61816131586961341330
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
1.663 Γ— 10¹⁰⁴(105-digit number)
16630107063437543990…61816131586961341329
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.663 Γ— 10¹⁰⁴(105-digit number)
16630107063437543990…61816131586961341331
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
3.326 Γ— 10¹⁰⁴(105-digit number)
33260214126875087981…23632263173922682659
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.326 Γ— 10¹⁰⁴(105-digit number)
33260214126875087981…23632263173922682661
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
6.652 Γ— 10¹⁰⁴(105-digit number)
66520428253750175963…47264526347845365319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.652 Γ— 10¹⁰⁴(105-digit number)
66520428253750175963…47264526347845365321
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
1.330 Γ— 10¹⁰⁡(106-digit number)
13304085650750035192…94529052695690730639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.330 Γ— 10¹⁰⁡(106-digit number)
13304085650750035192…94529052695690730641
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
2.660 Γ— 10¹⁰⁡(106-digit number)
26608171301500070385…89058105391381461279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.660 Γ— 10¹⁰⁡(106-digit number)
26608171301500070385…89058105391381461281
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 343996

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 5bc5c3faf53104e414a770b657b41e93d5dfff28a6a7cbe5827a989d0632021c

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 #343,996 on Chainz β†—
Circulating Supply:57,841,778 XPMΒ·at block #6,824,713 Β· updates every 60s
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