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Block #146,746

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2013, 4:47:26 PM Β· Difficulty 9.8491 Β· 6,680,336 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
13b2579553a7ae595324a86fb178fa016a573b151c78430d37dffdd30f321f68
View on Chainz β†—

Height

#146,746

Difficulty

9.849114

Transactions

1

Size

199 B

Version

2

Bits

09d95f8a

Nonce

77,879

Timestamp

9/2/2013, 4:47:26 PM

Confirmations

6,680,336

Merkle Root

dcaab2c1c6a6ff852eb8a25febc4cb8cde9397ea6368fb672d95e6d16a325691
Transactions (1)
Coinbasedcaab2c1c6a6ff…95e6d16a325691
1 in β†’ 1 out10.2900 XPM109 B
AM2aZLZw…B8dSVS4x
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.

3.923 Γ— 10⁹⁴(95-digit number)
39234834446032188419…21037425046554821120
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
3.923 Γ— 10⁹⁴(95-digit number)
39234834446032188419…21037425046554821119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.923 Γ— 10⁹⁴(95-digit number)
39234834446032188419…21037425046554821121
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
7.846 Γ— 10⁹⁴(95-digit number)
78469668892064376838…42074850093109642239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.846 Γ— 10⁹⁴(95-digit number)
78469668892064376838…42074850093109642241
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
1.569 Γ— 10⁹⁡(96-digit number)
15693933778412875367…84149700186219284479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.569 Γ— 10⁹⁡(96-digit number)
15693933778412875367…84149700186219284481
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
3.138 Γ— 10⁹⁡(96-digit number)
31387867556825750735…68299400372438568959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.138 Γ— 10⁹⁡(96-digit number)
31387867556825750735…68299400372438568961
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
6.277 Γ— 10⁹⁡(96-digit number)
62775735113651501470…36598800744877137919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 146746

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 13b2579553a7ae595324a86fb178fa016a573b151c78430d37dffdd30f321f68

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 #146,746 on Chainz β†—
Circulating Supply:57,860,841 XPMΒ·at block #6,827,081 Β· updates every 60s
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