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Block #346,103

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2014, 8:50:38 AM Β· Difficulty 10.2181 Β· 6,478,496 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b7e77d82944c711e1b8a59656c6098aa724f4cab214cebb39c690dac71513771
View on Chainz β†—

Height

#346,103

Difficulty

10.218073

Transactions

1

Size

208 B

Version

2

Bits

0a37d3a7

Nonce

77,316

Timestamp

1/6/2014, 8:50:38 AM

Confirmations

6,478,496

Merkle Root

ce35391b9b9b27596009247bc1e60b031f279d43fc30aff8c9b6f6008baf820f
Transactions (1)
Coinbasece35391b9b9b27…b6f6008baf820f
1 in β†’ 1 out9.5600 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.

1.267 Γ— 10⁹⁹(100-digit number)
12678478807709705896…94536445686590136320
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
1.267 Γ— 10⁹⁹(100-digit number)
12678478807709705896…94536445686590136319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.267 Γ— 10⁹⁹(100-digit number)
12678478807709705896…94536445686590136321
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
2.535 Γ— 10⁹⁹(100-digit number)
25356957615419411792…89072891373180272639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.535 Γ— 10⁹⁹(100-digit number)
25356957615419411792…89072891373180272641
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
5.071 Γ— 10⁹⁹(100-digit number)
50713915230838823585…78145782746360545279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.071 Γ— 10⁹⁹(100-digit number)
50713915230838823585…78145782746360545281
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
1.014 Γ— 10¹⁰⁰(101-digit number)
10142783046167764717…56291565492721090559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.014 Γ— 10¹⁰⁰(101-digit number)
10142783046167764717…56291565492721090561
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
2.028 Γ— 10¹⁰⁰(101-digit number)
20285566092335529434…12583130985442181119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.028 Γ— 10¹⁰⁰(101-digit number)
20285566092335529434…12583130985442181121
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
4.057 Γ— 10¹⁰⁰(101-digit number)
40571132184671058868…25166261970884362239
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 346103

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 b7e77d82944c711e1b8a59656c6098aa724f4cab214cebb39c690dac71513771

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 #346,103 on Chainz β†—
Circulating Supply:57,840,861 XPMΒ·at block #6,824,598 Β· updates every 60s
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