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Block #175,528

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 8:57:02 AM · Difficulty 9.8636 · 6,614,571 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a75b1c0cd29b6796306e8b675db7f7b3abd93cda8ad7ed2602502cf2b1492e94

View on Chainz ↗

Height

#175,528

Difficulty

9.863646

Transactions

Size

1.16 KB

Version

Bits

09dd17ef

Nonce

22,671

Timestamp

9/22/2013, 8:57:02 AM

Confirmations

6,614,571

Merkle Root

79f36c97e9ab7a750c0b113ab8e6450de5c071dd6d3ef12eb6b53b3b79290755

Transactions (4)

Coinbase8df64651266dfb…f251c13907f9a5

1 in → 1 out10.2900 XPM109 B

AKvnYqzV…YStNr4s5

d9e557deb11f9e…e56e7ede2ab908

4 in → 2 out52.1300 XPM535 B

APfmPqHz…Z6JBpNUw AMGFGp7t…dXQoA5sF

063294b74ee72e…53cb07ad68c0f6

1 in → 2 out10.2500 XPM226 B

AYU27B6h…gHyyevcz AQkCXVaL…iN1GB5D2

87b356003af3c7…0ff4ad759a5793

1 in → 2 out4.0865 XPM227 B

ARXSrG7z…CRW69WR4 AeZLuj6j…RKa4Mx7k

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.740 × 10⁹²(93-digit number)

47402369913468622127…62004054311077769070

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

4.740 × 10⁹²(93-digit number)

47402369913468622127…62004054311077769069

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.740 × 10⁹²(93-digit number)

47402369913468622127…62004054311077769071

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

9.480 × 10⁹²(93-digit number)

94804739826937244255…24008108622155538139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.480 × 10⁹²(93-digit number)

94804739826937244255…24008108622155538141

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.896 × 10⁹³(94-digit number)

18960947965387448851…48016217244311076279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.896 × 10⁹³(94-digit number)

18960947965387448851…48016217244311076281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.792 × 10⁹³(94-digit number)

37921895930774897702…96032434488622152559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.792 × 10⁹³(94-digit number)

37921895930774897702…96032434488622152561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

7.584 × 10⁹³(94-digit number)

75843791861549795404…92064868977244305119

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — 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 →

★☆☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 175528

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 a75b1c0cd29b6796306e8b675db7f7b3abd93cda8ad7ed2602502cf2b1492e94

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 → Debug Window → 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 #175,528 on Chainz ↗