Block #236,854

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 5:26:15 PM · Difficulty 9.9486 · 6,573,403 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

333574d8a6bf3d5c3ed3de882c80269729b052d8f2a85f726f9ee796ae0ad7dc

View on Chainz ↗

Height

#236,854

Difficulty

9.948575

Transactions

Size

1.36 KB

Version

Bits

09f2d5cf

Nonce

9,652

Timestamp

10/31/2013, 5:26:15 PM

Confirmations

6,573,403

Mined by

⛏️ P2SHAeL7UAFbYJxtsFPY1Wp7S8F2EUW9mPDyGL

Merkle Root

bbe918568e044b8141cc0d4f53bb6b386b686ca4fc4886d841eb4a67b98896a8

Transactions (4)

Coinbase33790cd700b559…367e3a29f802de

1 in → 2 out10.1300 XPM136 B

AeL7UAFb…W9mPDyGL AKNbfPoc…jfkpwAyL

5b00505150ce19…1fad5ea0505a0c

1 in → 1 out10.1800 XPM157 B

AWhXXrZV…erWALTNx

a64b73b3705113…5a6e264ba57c17

5 in → 2 out38.0313 XPM815 B

AQAvQSWZ…C9mFkvux ATkEiUNn…WJ2biSX5

1ec6cfc19f53f4…8a60e034f0c9ba

1 in → 1 out1.9933 XPM192 B

AXhMcKBp…Drzdc8Hw

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.

7.115 × 10⁹⁹(100-digit number)

71156474670106085431…29962601663803622399

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

7.115 × 10⁹⁹(100-digit number)

71156474670106085431…29962601663803622399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.115 × 10⁹⁹(100-digit number)

71156474670106085431…29962601663803622401

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

1.423 × 10¹⁰⁰(101-digit number)

14231294934021217086…59925203327607244799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.423 × 10¹⁰⁰(101-digit number)

14231294934021217086…59925203327607244801

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

2.846 × 10¹⁰⁰(101-digit number)

28462589868042434172…19850406655214489599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.846 × 10¹⁰⁰(101-digit number)

28462589868042434172…19850406655214489601

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

5.692 × 10¹⁰⁰(101-digit number)

56925179736084868344…39700813310428979199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.692 × 10¹⁰⁰(101-digit number)

56925179736084868344…39700813310428979201

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

1.138 × 10¹⁰¹(102-digit number)

11385035947216973668…79401626620857958399

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 #236,854

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