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Block #337,923

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/1/2014, 1:35:45 AM Β· Difficulty 10.1260 Β· 6,460,171 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7aea8c2ce6b74976503abf92f3a2a4a765f291fe568722496c13471b3b135a5f
View on Chainz β†—

Height

#337,923

Difficulty

10.126011

Transactions

1

Size

210 B

Version

2

Bits

0a20423d

Nonce

31,551

Timestamp

1/1/2014, 1:35:45 AM

Confirmations

6,460,171

Merkle Root

12c782c54e28d9ca75e8d1d2cfbf7e76ce258f9ecbf439bdce5f3606fd268bcb
Transactions (1)
Coinbase12c782c54e28d9…5f3606fd268bcb
1 in β†’ 1 out9.7400 XPM116 B
AbwWkWZt…kawDhufa
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.

2.560 Γ— 10¹⁰⁡(106-digit number)
25602305317486677046…96966745685577954240
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
2.560 Γ— 10¹⁰⁡(106-digit number)
25602305317486677046…96966745685577954239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.560 Γ— 10¹⁰⁡(106-digit number)
25602305317486677046…96966745685577954241
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
5.120 Γ— 10¹⁰⁡(106-digit number)
51204610634973354093…93933491371155908479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.120 Γ— 10¹⁰⁡(106-digit number)
51204610634973354093…93933491371155908481
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
1.024 Γ— 10¹⁰⁢(107-digit number)
10240922126994670818…87866982742311816959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.024 Γ— 10¹⁰⁢(107-digit number)
10240922126994670818…87866982742311816961
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
2.048 Γ— 10¹⁰⁢(107-digit number)
20481844253989341637…75733965484623633919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.048 Γ— 10¹⁰⁢(107-digit number)
20481844253989341637…75733965484623633921
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
4.096 Γ— 10¹⁰⁢(107-digit number)
40963688507978683274…51467930969247267839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.096 Γ— 10¹⁰⁢(107-digit number)
40963688507978683274…51467930969247267841
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
8.192 Γ— 10¹⁰⁢(107-digit number)
81927377015957366549…02935861938494535679
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 337923

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 7aea8c2ce6b74976503abf92f3a2a4a765f291fe568722496c13471b3b135a5f

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 #337,923 on Chainz β†—
Circulating Supply:57,628,751 XPMΒ·at block #6,798,093 Β· updates every 60s
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