Block #236,780

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 4:30:02 PM · Difficulty 9.9484 · 6,561,645 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

58535ab1a5505b225d7c8703d2b5fd582bd48bc510867c1d6dfac76e1f84f650

View on Chainz ↗

Height

#236,780

Difficulty

9.948377

Transactions

Size

1.94 KB

Version

Bits

09f2c8db

Nonce

3,973

Timestamp

10/31/2013, 4:30:02 PM

Confirmations

6,561,645

Mined by

⛏️ P2SHAeL7UAFbYJxtsFPY1Wp7S8F2EUW9mPDyGL

Merkle Root

fa86c9286a410a8ed1a74cd68e5067c8c07b684032abe14a9f8af57391d69ea4

Transactions (5)

Coinbase83ec30ba5a93c4…00fa0fdfcfeaa4

1 in → 2 out10.1300 XPM137 B

AeL7UAFb…W9mPDyGL AKNbfPoc…jfkpwAyL

9738b1ab76afa6…f1b16bebd1747d

2 in → 2 out33.0100 XPM374 B

AQuU7aTa…JYv7MTNX AHibBzVv…7iNiYxeu

779d8f919eab53…eb4dc6cd0e5be8

5 in → 2 out50.0157 XPM818 B

AdpSA37n…Mr8rabgt APRtb3rM…uzrCr2pm

59ee96187aeea6…b0d0a9bc02d54e

2 in → 2 out20.1900 XPM374 B

AFsMW6dF…Z3wb5bBq AYdEZujQ…eq6LiuA1

4b5fda30a74649…c25de0a67757c7

1 in → 1 out174.6438 XPM191 B

AZd4wZhL…CYkAnJ2t

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.

1.011 × 10¹⁰¹(102-digit number)

10118202143759052446…10717271588245668479

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

1.011 × 10¹⁰¹(102-digit number)

10118202143759052446…10717271588245668479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.011 × 10¹⁰¹(102-digit number)

10118202143759052446…10717271588245668481

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

2.023 × 10¹⁰¹(102-digit number)

20236404287518104892…21434543176491336959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.023 × 10¹⁰¹(102-digit number)

20236404287518104892…21434543176491336961

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

4.047 × 10¹⁰¹(102-digit number)

40472808575036209784…42869086352982673919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.047 × 10¹⁰¹(102-digit number)

40472808575036209784…42869086352982673921

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

8.094 × 10¹⁰¹(102-digit number)

80945617150072419568…85738172705965347839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.094 × 10¹⁰¹(102-digit number)

80945617150072419568…85738172705965347841

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

1.618 × 10¹⁰²(103-digit number)

16189123430014483913…71476345411930695679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.618 × 10¹⁰²(103-digit number)

16189123430014483913…71476345411930695681

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