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Block #345,915

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2014, 6:07:00 AM Β· Difficulty 10.2140 Β· 6,454,903 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8e6072c83ff7cdc619cf34b3e736858363aeb7b81fb9bdb718fa3759f0bfd152
View on Chainz β†—

Height

#345,915

Difficulty

10.214050

Transactions

1

Size

208 B

Version

2

Bits

0a36cbf6

Nonce

4,723

Timestamp

1/6/2014, 6:07:00 AM

Confirmations

6,454,903

Merkle Root

6519d5a3a77129897b9876c06cf0746bf916a28f74ff98d7a1ed0cf7c858447c
Transactions (1)
Coinbase6519d5a3a77129…ed0cf7c858447c
1 in β†’ 1 out9.5700 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.

4.513 Γ— 10⁹⁹(100-digit number)
45130346885576852257…23060933302454159360
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
4.513 Γ— 10⁹⁹(100-digit number)
45130346885576852257…23060933302454159359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.513 Γ— 10⁹⁹(100-digit number)
45130346885576852257…23060933302454159361
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
9.026 Γ— 10⁹⁹(100-digit number)
90260693771153704515…46121866604908318719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.026 Γ— 10⁹⁹(100-digit number)
90260693771153704515…46121866604908318721
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
1.805 Γ— 10¹⁰⁰(101-digit number)
18052138754230740903…92243733209816637439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.805 Γ— 10¹⁰⁰(101-digit number)
18052138754230740903…92243733209816637441
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
3.610 Γ— 10¹⁰⁰(101-digit number)
36104277508461481806…84487466419633274879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.610 Γ— 10¹⁰⁰(101-digit number)
36104277508461481806…84487466419633274881
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
7.220 Γ— 10¹⁰⁰(101-digit number)
72208555016922963612…68974932839266549759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.220 Γ— 10¹⁰⁰(101-digit number)
72208555016922963612…68974932839266549761
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 345915

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 8e6072c83ff7cdc619cf34b3e736858363aeb7b81fb9bdb718fa3759f0bfd152

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 #345,915 on Chainz β†—
Circulating Supply:57,650,600 XPMΒ·at block #6,800,817 Β· updates every 60s
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