Block #103,234

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/7/2013, 12:11:22 PM · Difficulty 9.5194 · 6,714,080 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

532ac4a562b5f4e5de88d737a719a1ca95a7fe6e8e7199b83e6fbe53fdfc5cda

View on Chainz ↗

Height

#103,234

Difficulty

9.519420

Transactions

Size

629 B

Version

Bits

0984f8b4

Nonce

159,808

Timestamp

8/7/2013, 12:11:22 PM

Confirmations

6,714,080

Mined by

⛏️ P2SHALfSa1cW7NJcZC5cEicdo7cA2yBRMoBka6

Merkle Root

4a4a43fc66e986fe0183f2e2adfe722ff9fb67fc7b4bdbe1fe0ba57d5b521506

Transactions (3)

Coinbasec23d2ec8d669e3…beee14123a9c11

1 in → 1 out11.0400 XPM109 B

ALfSa1cW…BRMoBka6

01c4d1ce21b8cb…88225cd332b914

2 in → 1 out22.9200 XPM270 B

AG9fC8vT…6ZUAGf72

34cbb45bc1fc40…c729fcf19d36e3

1 in → 1 out11.2800 XPM159 B

AYnxGXr3…YuBfvEPk

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.

1.076 × 10⁹⁸(99-digit number)

10765377680684252090…60976130260456965779

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

1.076 × 10⁹⁸(99-digit number)

10765377680684252090…60976130260456965779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.076 × 10⁹⁸(99-digit number)

10765377680684252090…60976130260456965781

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

2.153 × 10⁹⁸(99-digit number)

21530755361368504181…21952260520913931559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.153 × 10⁹⁸(99-digit number)

21530755361368504181…21952260520913931561

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

4.306 × 10⁹⁸(99-digit number)

43061510722737008362…43904521041827863119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.306 × 10⁹⁸(99-digit number)

43061510722737008362…43904521041827863121

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

8.612 × 10⁹⁸(99-digit number)

86123021445474016725…87809042083655726239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.612 × 10⁹⁸(99-digit number)

86123021445474016725…87809042083655726241

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

1.722 × 10⁹⁹(100-digit number)

17224604289094803345…75618084167311452479

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 #103,234

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