Block #127,815

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/21/2013, 7:24:42 PM · Difficulty 9.7830 · 6,688,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7173579687f635fb4f41170c424b9a239845f7053f7c5bb19a949910a06babc

View on Chainz ↗

Height

#127,815

Difficulty

9.783000

Transactions

Size

393 B

Version

Bits

09c872b8

Nonce

120,683

Timestamp

8/21/2013, 7:24:42 PM

Confirmations

6,688,286

Mined by

⛏️ P2SHASki8pmAYiSmpQcpe6L3Yu14B9Dwetzr7b

Merkle Root

72ee18a1d242859483958c9fd7a7036120e36fdce5692ac7aef6450d6e920653

Transactions (2)

Coinbasee6a079db5bd835…08e6076d3b327b

1 in → 1 out10.4400 XPM109 B

ASki8pmA…Dwetzr7b

0acebdcbead5ce…5bd1dffa14dbb3

1 in → 2 out10.4500 XPM193 B

AGZvBxxa…shhkwtTn APpvZocX…BasLAX69

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.

5.527 × 10⁹⁷(98-digit number)

55275437213017673370…30343087495367545459

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

5.527 × 10⁹⁷(98-digit number)

55275437213017673370…30343087495367545459

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.527 × 10⁹⁷(98-digit number)

55275437213017673370…30343087495367545461

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

1.105 × 10⁹⁸(99-digit number)

11055087442603534674…60686174990735090919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.105 × 10⁹⁸(99-digit number)

11055087442603534674…60686174990735090921

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

2.211 × 10⁹⁸(99-digit number)

22110174885207069348…21372349981470181839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.211 × 10⁹⁸(99-digit number)

22110174885207069348…21372349981470181841

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

4.422 × 10⁹⁸(99-digit number)

44220349770414138696…42744699962940363679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.422 × 10⁹⁸(99-digit number)

44220349770414138696…42744699962940363681

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

8.844 × 10⁹⁸(99-digit number)

88440699540828277393…85489399925880727359

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 #127,815

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