Block #175,949

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/22/2013, 3:34:37 PM · Difficulty 9.8642 · 6,641,478 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

98140967c1fccfde8703ed9f0f6d93eba27c6b3043675da4a29ab08ae51ec8ef

View on Chainz ↗

Height

#175,949

Difficulty

9.864201

Transactions

Size

723 B

Version

Bits

09dd3c4f

Nonce

13,730

Timestamp

9/22/2013, 3:34:37 PM

Confirmations

6,641,478

Mined by

⛏️ P2SHANuF339wP4ayd5BSmDmS68NREGiYPZq6Rh

Merkle Root

4939cef50982a28599a9b8dc4e9ce541325d3c0e519fe6ab594277e3cdd5f73c

Transactions (2)

Coinbasedd62ee1374c95e…596a66b54369ba

1 in → 1 out10.2700 XPM109 B

ANuF339w…iYPZq6Rh

73cc64156419b9…74ea8ee80bb80c

3 in → 2 out50.0268 XPM522 B

AMW1R2xY…HnG2vF3J AV9avvvi…Fz8uwxS7

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.

1.822 × 10⁹⁹(100-digit number)

18224386909867828533…57806686832770047999

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

1.822 × 10⁹⁹(100-digit number)

18224386909867828533…57806686832770047999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.822 × 10⁹⁹(100-digit number)

18224386909867828533…57806686832770048001

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

3.644 × 10⁹⁹(100-digit number)

36448773819735657066…15613373665540095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.644 × 10⁹⁹(100-digit number)

36448773819735657066…15613373665540096001

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

7.289 × 10⁹⁹(100-digit number)

72897547639471314132…31226747331080191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.289 × 10⁹⁹(100-digit number)

72897547639471314132…31226747331080192001

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

1.457 × 10¹⁰⁰(101-digit number)

14579509527894262826…62453494662160383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.457 × 10¹⁰⁰(101-digit number)

14579509527894262826…62453494662160384001

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

2.915 × 10¹⁰⁰(101-digit number)

29159019055788525652…24906989324320767999

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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Cross-reference on Chainz Explorer

Block #175,949

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