Block #235,424

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 10:07:49 PM · Difficulty 9.9456 · 6,559,469 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e1e53a532b93d75a6aafb4ed6c4c641ee8321c6238eb2af2eac22bf7beba542c

View on Chainz ↗

Height

#235,424

Difficulty

9.945627

Transactions

Size

2.04 KB

Version

Bits

09f214a1

Nonce

4,718

Timestamp

10/30/2013, 10:07:49 PM

Confirmations

6,559,469

Mined by

⛏️ Rq:ANUaggy4nFSyDVA2nmSGYrEQvJMWdrertQ

Merkle Root

00e5fc6ece97d2a52b1e4d94f75e3551fc3a53889225a62990ecc7fe11adb31c

Transactions (1)

Coinbase00e5fc6ece97d2…ecc7fe11adb31c

1 in → 57 out10.0700 XPM1.95 KB

ANUaggy4…MWdrertQ AYckRkCF…TgDe5VSp AeZmMFY8…mjAy5Mi4 ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC

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.

8.091 × 10⁹⁸(99-digit number)

80914437478349498571…63646034324128578559

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

8.091 × 10⁹⁸(99-digit number)

80914437478349498571…63646034324128578559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.091 × 10⁹⁸(99-digit number)

80914437478349498571…63646034324128578561

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

1.618 × 10⁹⁹(100-digit number)

16182887495669899714…27292068648257157119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.618 × 10⁹⁹(100-digit number)

16182887495669899714…27292068648257157121

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

3.236 × 10⁹⁹(100-digit number)

32365774991339799428…54584137296514314239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.236 × 10⁹⁹(100-digit number)

32365774991339799428…54584137296514314241

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

6.473 × 10⁹⁹(100-digit number)

64731549982679598857…09168274593028628479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.473 × 10⁹⁹(100-digit number)

64731549982679598857…09168274593028628481

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

1.294 × 10¹⁰⁰(101-digit number)

12946309996535919771…18336549186057256959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.294 × 10¹⁰⁰(101-digit number)

12946309996535919771…18336549186057256961

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