Block #241,647

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 8:02:08 AM · Difficulty 9.9583 · 6,554,252 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c594dc4f75e9e2062727b0977645c1e698c309a978ababa5e210f47c3cea8b79

View on Chainz ↗

Height

#241,647

Difficulty

9.958302

Transactions

Size

1.67 KB

Version

Bits

09f55344

Nonce

291,288

Timestamp

11/3/2013, 8:02:08 AM

Confirmations

6,554,252

Mined by

⛏️ RvoAT3ATVPtjfng878mf7ratQVkQGQw6x41k1

Merkle Root

76af50f622bf0d9f689daaee5a8d11ebdc82e75c19f39a454d7323f306b25fce

Transactions (1)

Coinbase76af50f622bf0d…7323f306b25fce

1 in → 46 out10.0500 XPM1.59 KB

AT3ATVPt…Qw6x41k1 ANuKx9Ke…wm7nrBRq AabHNb1B…GRoingRy AJaGRnaj…iCHGoy6E AeZmMFY8…mjAy5Mi4

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.

1.990 × 10⁹⁰(91-digit number)

19900085814043169544…43407702460746608639

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

1.990 × 10⁹⁰(91-digit number)

19900085814043169544…43407702460746608639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.990 × 10⁹⁰(91-digit number)

19900085814043169544…43407702460746608641

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

3.980 × 10⁹⁰(91-digit number)

39800171628086339088…86815404921493217279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.980 × 10⁹⁰(91-digit number)

39800171628086339088…86815404921493217281

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

7.960 × 10⁹⁰(91-digit number)

79600343256172678177…73630809842986434559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.960 × 10⁹⁰(91-digit number)

79600343256172678177…73630809842986434561

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

1.592 × 10⁹¹(92-digit number)

15920068651234535635…47261619685972869119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.592 × 10⁹¹(92-digit number)

15920068651234535635…47261619685972869121

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

3.184 × 10⁹¹(92-digit number)

31840137302469071270…94523239371945738239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.184 × 10⁹¹(92-digit number)

31840137302469071270…94523239371945738241

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