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Block #151,187

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 12:48:20 PM Β· Difficulty 9.8598 Β· 6,675,386 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d26c6bcab5edd750764c55232a2f6f199397b863cf1f6699905f72f11d8e80f
View on Chainz β†—

Height

#151,187

Difficulty

9.859792

Transactions

1

Size

197 B

Version

2

Bits

09dc1b53

Nonce

83,128

Timestamp

9/5/2013, 12:48:20 PM

Confirmations

6,675,386

Merkle Root

c19e5d504f524f35d9049284c129ad38a6fed541c7eb77eff44de4fac86ae4ca
Transactions (1)
Coinbasec19e5d504f524f…4de4fac86ae4ca
1 in β†’ 1 out10.2700 XPM109 B
AJNnxqXc…Hj9ayqaW
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.

3.532 Γ— 10⁹⁰(91-digit number)
35326825460197174972…99875449811852929280
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
3.532 Γ— 10⁹⁰(91-digit number)
35326825460197174972…99875449811852929279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.532 Γ— 10⁹⁰(91-digit number)
35326825460197174972…99875449811852929281
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
7.065 Γ— 10⁹⁰(91-digit number)
70653650920394349944…99750899623705858559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.065 Γ— 10⁹⁰(91-digit number)
70653650920394349944…99750899623705858561
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
1.413 Γ— 10⁹¹(92-digit number)
14130730184078869988…99501799247411717119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.413 Γ— 10⁹¹(92-digit number)
14130730184078869988…99501799247411717121
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
2.826 Γ— 10⁹¹(92-digit number)
28261460368157739977…99003598494823434239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.826 Γ— 10⁹¹(92-digit number)
28261460368157739977…99003598494823434241
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
5.652 Γ— 10⁹¹(92-digit number)
56522920736315479955…98007196989646868479
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 151187

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 4d26c6bcab5edd750764c55232a2f6f199397b863cf1f6699905f72f11d8e80f

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 #151,187 on Chainz β†—
Circulating Supply:57,856,733 XPMΒ·at block #6,826,572 Β· updates every 60s
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