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Block #154,911

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2013, 11:54:17 PM Β· Difficulty 9.8648 Β· 6,640,908 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
859e123ccb7cbcd931d181839c10d9aa804c20abda2ef95f2c10099c4f64b21b
View on Chainz β†—

Height

#154,911

Difficulty

9.864774

Transactions

1

Size

199 B

Version

2

Bits

09dd61ce

Nonce

21,161

Timestamp

9/7/2013, 11:54:17 PM

Confirmations

6,640,908

Merkle Root

b027373c548161d558f981545672179292055db63e6c3f12ce67889427739a43
Transactions (1)
Coinbaseb027373c548161…67889427739a43
1 in β†’ 1 out10.2600 XPM109 B
AJhMUuMT…Ro6UPfNc
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.

1.869 Γ— 10⁹⁴(95-digit number)
18691242105055431623…00051897090682168960
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
1.869 Γ— 10⁹⁴(95-digit number)
18691242105055431623…00051897090682168959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.869 Γ— 10⁹⁴(95-digit number)
18691242105055431623…00051897090682168961
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
3.738 Γ— 10⁹⁴(95-digit number)
37382484210110863247…00103794181364337919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.738 Γ— 10⁹⁴(95-digit number)
37382484210110863247…00103794181364337921
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
7.476 Γ— 10⁹⁴(95-digit number)
74764968420221726494…00207588362728675839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.476 Γ— 10⁹⁴(95-digit number)
74764968420221726494…00207588362728675841
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
1.495 Γ— 10⁹⁡(96-digit number)
14952993684044345298…00415176725457351679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.495 Γ— 10⁹⁡(96-digit number)
14952993684044345298…00415176725457351681
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
2.990 Γ— 10⁹⁡(96-digit number)
29905987368088690597…00830353450914703359
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 154911

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 859e123ccb7cbcd931d181839c10d9aa804c20abda2ef95f2c10099c4f64b21b

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 #154,911 on Chainz β†—
Circulating Supply:57,610,634 XPMΒ·at block #6,795,818 Β· updates every 60s
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