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Block #41,145

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2013, 4:09:39 PM Β· Difficulty 8.4990 Β· 6,759,111 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ab7ba6e6adb576f2d9875dfbf56b5255e30b0999bf6bc31a67e5a448b90ca4f
View on Chainz β†—

Height

#41,145

Difficulty

8.499026

Transactions

3

Size

632 B

Version

2

Bits

087fc029

Nonce

187

Timestamp

7/14/2013, 4:09:39 PM

Confirmations

6,759,111

Merkle Root

d71bf84d0357cd7270738a89ff4fbf0b7b947cf01cd089c49c9062abddd1eec2
Transactions (3)
Coinbase484febf29aaea9…8a5cf5ee118015
1 in β†’ 1 out13.8500 XPM110 B
Aeg73xq9…k2T5gw66
e297526d7affa0…354645f2b37d1c
2 in β†’ 1 out31.2700 XPM271 B
AG43TCYA…UW1AUz7e
9c1256eb5bbbd5…2ebca116051bca
1 in β†’ 1 out15.6200 XPM158 B
AJV9J7t5…G9F5PrK8
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.

1.422 Γ— 10¹⁰²(103-digit number)
14229808598092256133…40283744286918969960
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
1.422 Γ— 10¹⁰²(103-digit number)
14229808598092256133…40283744286918969959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.422 Γ— 10¹⁰²(103-digit number)
14229808598092256133…40283744286918969961
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
2.845 Γ— 10¹⁰²(103-digit number)
28459617196184512266…80567488573837939919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.845 Γ— 10¹⁰²(103-digit number)
28459617196184512266…80567488573837939921
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
5.691 Γ— 10¹⁰²(103-digit number)
56919234392369024533…61134977147675879839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.691 Γ— 10¹⁰²(103-digit number)
56919234392369024533…61134977147675879841
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
1.138 Γ— 10¹⁰³(104-digit number)
11383846878473804906…22269954295351759679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.138 Γ— 10¹⁰³(104-digit number)
11383846878473804906…22269954295351759681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8
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 41145

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 1ab7ba6e6adb576f2d9875dfbf56b5255e30b0999bf6bc31a67e5a448b90ca4f

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 #41,145 on Chainz β†—
Circulating Supply:57,646,103 XPMΒ·at block #6,800,255 Β· updates every 60s
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