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Block #175,256

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/22/2013, 4:19:19 AM Β· Difficulty 9.8637 Β· 6,650,921 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
12eb6308f88d6b5b5ca2741548143a5fdd7f0c7c26d1456b679a5cb3517b2158
View on Chainz β†—

Height

#175,256

Difficulty

9.863656

Transactions

1

Size

204 B

Version

2

Bits

09dd188d

Nonce

46,721

Timestamp

9/22/2013, 4:19:19 AM

Confirmations

6,650,921

Merkle Root

bb07776e44d3cc3417e58d9cb207ef8c5ab731b7fc9139add88eb54e1ce377bb
Transactions (1)
Coinbasebb07776e44d3cc…8eb54e1ce377bb
1 in β†’ 1 out10.2600 XPM112 B
AcLBm5Z9…S683d7c3
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.

3.934 Γ— 10¹⁰⁰(101-digit number)
39340637380420550193…86157554884615140400
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
3.934 Γ— 10¹⁰⁰(101-digit number)
39340637380420550193…86157554884615140399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.934 Γ— 10¹⁰⁰(101-digit number)
39340637380420550193…86157554884615140401
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
7.868 Γ— 10¹⁰⁰(101-digit number)
78681274760841100386…72315109769230280799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.868 Γ— 10¹⁰⁰(101-digit number)
78681274760841100386…72315109769230280801
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
1.573 Γ— 10¹⁰¹(102-digit number)
15736254952168220077…44630219538460561599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.573 Γ— 10¹⁰¹(102-digit number)
15736254952168220077…44630219538460561601
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
3.147 Γ— 10¹⁰¹(102-digit number)
31472509904336440154…89260439076921123199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.147 Γ— 10¹⁰¹(102-digit number)
31472509904336440154…89260439076921123201
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
6.294 Γ— 10¹⁰¹(102-digit number)
62945019808672880308…78520878153842246399
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 175256

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 12eb6308f88d6b5b5ca2741548143a5fdd7f0c7c26d1456b679a5cb3517b2158

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 #175,256 on Chainz β†—
Circulating Supply:57,853,545 XPMΒ·at block #6,826,176 Β· updates every 60s
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