Block #172,835

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/20/2013, 1:29:30 PM · Difficulty 9.8610 · 6,653,751 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f12d3cf85c15365ba0533660bf651d71f4412a311540a2fe96b370a8fcc2553d

View on Chainz ↗

Height

#172,835

Difficulty

9.861047

Transactions

Size

1018 B

Version

Bits

09dc6d91

Nonce

72,714

Timestamp

9/20/2013, 1:29:30 PM

Confirmations

6,653,751

Mined by

⛏️ P2SHATa7vj12fjaqe9KXPyVFZDtmSNCHr9Mn3k

Merkle Root

7d83c4d36774f744e85a482f5b873dbe74c03bc8517c10de36626e014554bcc2

Transactions (2)

Coinbasea7468c0e7bc317…11be9f87ff3e90

1 in → 1 out10.2800 XPM109 B

ATa7vj12…CHr9Mn3k

8d0bb6a15992dc…562d5109faa263

5 in → 2 out700.2259 XPM818 B

ATqsEPCu…wB6rsyPo Aet6gj1V…rUGvKhLb

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.

5.800 × 10⁹⁷(98-digit number)

58008355091544724876…53156625175206809599

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

5.800 × 10⁹⁷(98-digit number)

58008355091544724876…53156625175206809599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.800 × 10⁹⁷(98-digit number)

58008355091544724876…53156625175206809601

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

1.160 × 10⁹⁸(99-digit number)

11601671018308944975…06313250350413619199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.160 × 10⁹⁸(99-digit number)

11601671018308944975…06313250350413619201

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

2.320 × 10⁹⁸(99-digit number)

23203342036617889950…12626500700827238399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.320 × 10⁹⁸(99-digit number)

23203342036617889950…12626500700827238401

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

4.640 × 10⁹⁸(99-digit number)

46406684073235779901…25253001401654476799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.640 × 10⁹⁸(99-digit number)

46406684073235779901…25253001401654476801

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

9.281 × 10⁹⁸(99-digit number)

92813368146471559802…50506002803308953599

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 #172,835

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