Block #189,134

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/1/2013, 3:16:36 PM · Difficulty 9.8722 · 6,628,457 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

800420fd71c5a3e7b0845b61cfbe32b1326d2a2754ac25b8f29575c9dbec49bb

View on Chainz ↗

Height

#189,134

Difficulty

9.872235

Transactions

Size

2.63 KB

Version

Bits

09df4acf

Nonce

92,522

Timestamp

10/1/2013, 3:16:36 PM

Confirmations

6,628,457

Mined by

⛏️ P2SHATK4r8GhoVczEZqtspX4UTeEK5Usic4A9N

Merkle Root

51a0d7528348c0b57836660b17e9a62a772efa77070843c5ec3c4f67b14ca0ac

Transactions (5)

Coinbase9507bd8435eed2…259c84334ead78

1 in → 1 out10.3000 XPM109 B

ATK4r8Gh…Usic4A9N

dbd40ff4260863…b7331b0654e964

8 in → 1 out17.0460 XPM1.20 KB

AS85p8Qm…8YtNRCXe

ad6e686e6dce54…9bdc473dab59f4

1 in → 2 out1.9900 XPM225 B

Ae9doQb4…PiPe4nnu AYwmNUt6…591RoFn4

ba6976490c95aa…ff2aff8fe76266

1 in → 2 out8.2264 XPM225 B

AH4k3yjN…PUFV6WdB AdUEo83g…L3g1RcmX

417aa041d3e7b2…636e4c10cfa27c

5 in → 2 out2.0149 XPM818 B

ANGYFzvP…xtdQQN3D ANhqtMro…pTJyU7NY

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.

3.798 × 10⁹⁵(96-digit number)

37986385642159865261…75554647924590847999

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

3.798 × 10⁹⁵(96-digit number)

37986385642159865261…75554647924590847999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.798 × 10⁹⁵(96-digit number)

37986385642159865261…75554647924590848001

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

7.597 × 10⁹⁵(96-digit number)

75972771284319730522…51109295849181695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.597 × 10⁹⁵(96-digit number)

75972771284319730522…51109295849181696001

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

1.519 × 10⁹⁶(97-digit number)

15194554256863946104…02218591698363391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.519 × 10⁹⁶(97-digit number)

15194554256863946104…02218591698363392001

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

3.038 × 10⁹⁶(97-digit number)

30389108513727892209…04437183396726783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.038 × 10⁹⁶(97-digit number)

30389108513727892209…04437183396726784001

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

6.077 × 10⁹⁶(97-digit number)

60778217027455784418…08874366793453567999

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 #189,134

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