Block #190,484

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/2/2013, 12:39:24 PM · Difficulty 9.8741 · 6,619,650 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

938c2e2013efe58c65219498c5d6e253887416943b7aba1c6fe033ea1b7b5579

View on Chainz ↗

Height

#190,484

Difficulty

9.874120

Transactions

Size

1016 B

Version

Bits

09dfc64f

Nonce

203,758

Timestamp

10/2/2013, 12:39:24 PM

Confirmations

6,619,650

Mined by

⛏️ P2SHAaHga9xHgXGGLNGmefbcfen5UHDoJDm7Qz

Merkle Root

e3322bed7ded24958c56a1a8293006b11f5f5fd0e3aaa9a8796bcf3dc30697ac

Transactions (2)

Coinbaseb57f98aa2352a1…c655f10b67714e

1 in → 1 out10.2500 XPM109 B

AaHga9xH…DoJDm7Qz

c7a8934e9ce6b2…cc90bad4153c94

5 in → 2 out10.9700 XPM818 B

ALpthvGg…D1g5z4CT ARjecwig…s2xRHf2A

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.

1.683 × 10⁹³(94-digit number)

16837316648742838063…79864622003369800639

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

1.683 × 10⁹³(94-digit number)

16837316648742838063…79864622003369800639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.683 × 10⁹³(94-digit number)

16837316648742838063…79864622003369800641

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

3.367 × 10⁹³(94-digit number)

33674633297485676127…59729244006739601279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.367 × 10⁹³(94-digit number)

33674633297485676127…59729244006739601281

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

6.734 × 10⁹³(94-digit number)

67349266594971352254…19458488013479202559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.734 × 10⁹³(94-digit number)

67349266594971352254…19458488013479202561

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

1.346 × 10⁹⁴(95-digit number)

13469853318994270450…38916976026958405119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.346 × 10⁹⁴(95-digit number)

13469853318994270450…38916976026958405121

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

2.693 × 10⁹⁴(95-digit number)

26939706637988540901…77833952053916810239

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 #190,484

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