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Block #346,554

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/6/2014, 3:13:00 PM Β· Difficulty 10.2285 Β· 6,480,586 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2fba2ff8cfa7ce9e5c10f0996dc1e4dd07d5413ed4758632f534b699622e4dee
View on Chainz β†—

Height

#346,554

Difficulty

10.228525

Transactions

1

Size

206 B

Version

2

Bits

0a3a80a0

Nonce

87,760

Timestamp

1/6/2014, 3:13:00 PM

Confirmations

6,480,586

Merkle Root

b1d8c6d7416536e191bbca5d6884f235a3bf0a5588e0a9ef65b536499e094a84
Transactions (1)
Coinbaseb1d8c6d7416536…b536499e094a84
1 in β†’ 1 out9.5400 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.

1.004 Γ— 10⁹⁡(96-digit number)
10040385209431587461…53389918635278543760
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
1.004 Γ— 10⁹⁡(96-digit number)
10040385209431587461…53389918635278543759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.004 Γ— 10⁹⁡(96-digit number)
10040385209431587461…53389918635278543761
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
2.008 Γ— 10⁹⁡(96-digit number)
20080770418863174922…06779837270557087519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.008 Γ— 10⁹⁡(96-digit number)
20080770418863174922…06779837270557087521
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
4.016 Γ— 10⁹⁡(96-digit number)
40161540837726349845…13559674541114175039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.016 Γ— 10⁹⁡(96-digit number)
40161540837726349845…13559674541114175041
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
8.032 Γ— 10⁹⁡(96-digit number)
80323081675452699690…27119349082228350079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.032 Γ— 10⁹⁡(96-digit number)
80323081675452699690…27119349082228350081
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
1.606 Γ— 10⁹⁢(97-digit number)
16064616335090539938…54238698164456700159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.606 Γ— 10⁹⁢(97-digit number)
16064616335090539938…54238698164456700161
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 346554

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 2fba2ff8cfa7ce9e5c10f0996dc1e4dd07d5413ed4758632f534b699622e4dee

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 #346,554 on Chainz β†—
Circulating Supply:57,861,301 XPMΒ·at block #6,827,139 Β· updates every 60s
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