Block #1,293,553

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/22/2015, 9:18:22 AM · Difficulty 10.8563 · 5,521,302 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8f53b8b6d43eaaaffeff89c1b50382b782b86f056f0cd4bc40adf30e7bfb2744

View on Chainz ↗

Height

#1,293,553

Difficulty

10.856334

Transactions

Size

2.24 KB

Version

Bits

0adb38b9

Nonce

101,201,582

Timestamp

10/22/2015, 9:18:22 AM

Confirmations

5,521,302

Mined by

⛏️ P2SHAdboh9aD3cqsAgEsaNaWuhKJhf9gP5Akij

Merkle Root

0f330ff4f62928d2643d2eb4d8bf629e78b5fd990b15aa40768d143d57ea5512

Transactions (5)

Coinbasecc67d749eef47a…d791941d2de040

1 in → 1 out8.5100 XPM110 B

Adboh9aD…9gP5Akij

360fd316b4608b…28f6cbcff58ea1

1 in → 2 out8.4800 XPM226 B

AdCKW2yL…TR8y6dav APaYVt8e…rPF99zd2

5af6d194243021…0ddf455d9ba1f0

1 in → 2 out8.4800 XPM225 B

ANFyz2m1…y53myfCL AeBwvm57…kL6E7ayF

ce04e02d6d2647…5d7fd3b32f2e47

6 in → 2 out40.0950 XPM968 B

Ada5sUyS…hq3xto92 AehmKUU3…MKRgTyGB

d384888e122546…3741c83d299a4c

4 in → 2 out10.0889 XPM672 B

AQoFZuro…BNU2Nqcm AKTd6ocn…Ewwo3nj2

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.

2.826 × 10⁹⁶(97-digit number)

28269594526252995822…54968713601533153279

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

2.826 × 10⁹⁶(97-digit number)

28269594526252995822…54968713601533153279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.826 × 10⁹⁶(97-digit number)

28269594526252995822…54968713601533153281

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

5.653 × 10⁹⁶(97-digit number)

56539189052505991645…09937427203066306559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.653 × 10⁹⁶(97-digit number)

56539189052505991645…09937427203066306561

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

1.130 × 10⁹⁷(98-digit number)

11307837810501198329…19874854406132613119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.130 × 10⁹⁷(98-digit number)

11307837810501198329…19874854406132613121

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

2.261 × 10⁹⁷(98-digit number)

22615675621002396658…39749708812265226239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.261 × 10⁹⁷(98-digit number)

22615675621002396658…39749708812265226241

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

4.523 × 10⁹⁷(98-digit number)

45231351242004793316…79499417624530452479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.523 × 10⁹⁷(98-digit number)

45231351242004793316…79499417624530452481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #1,293,553

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