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Block #327,138

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/24/2013, 8:14:45 AM Β· Difficulty 10.1785 Β· 6,468,994 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cb6c9e46094132ecfb698b22fde4843e4ae9daa9ca7cbc524f746420fca5ab59
View on Chainz β†—

Height

#327,138

Difficulty

10.178456

Transactions

1

Size

208 B

Version

2

Bits

0a2daf4b

Nonce

71,479

Timestamp

12/24/2013, 8:14:45 AM

Confirmations

6,468,994

Merkle Root

bd929803a335a70e85043eaa36696f83ef03b40715176ab1909280e7067d7ca4
Transactions (1)
Coinbasebd929803a335a7…9280e7067d7ca4
1 in β†’ 1 out9.6400 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.

9.469 Γ— 10⁹⁸(99-digit number)
94693845089241777757…07049681254416584000
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
9.469 Γ— 10⁹⁸(99-digit number)
94693845089241777757…07049681254416583999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.469 Γ— 10⁹⁸(99-digit number)
94693845089241777757…07049681254416584001
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
1.893 Γ— 10⁹⁹(100-digit number)
18938769017848355551…14099362508833167999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.893 Γ— 10⁹⁹(100-digit number)
18938769017848355551…14099362508833168001
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
3.787 Γ— 10⁹⁹(100-digit number)
37877538035696711103…28198725017666335999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.787 Γ— 10⁹⁹(100-digit number)
37877538035696711103…28198725017666336001
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
7.575 Γ— 10⁹⁹(100-digit number)
75755076071393422206…56397450035332671999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.575 Γ— 10⁹⁹(100-digit number)
75755076071393422206…56397450035332672001
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
1.515 Γ— 10¹⁰⁰(101-digit number)
15151015214278684441…12794900070665343999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.515 Γ— 10¹⁰⁰(101-digit number)
15151015214278684441…12794900070665344001
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 327138

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 cb6c9e46094132ecfb698b22fde4843e4ae9daa9ca7cbc524f746420fca5ab59

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 #327,138 on Chainz β†—
Circulating Supply:57,613,051 XPMΒ·at block #6,796,131 Β· updates every 60s
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