Block #410,244

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/18/2014, 10:41:24 PM · Difficulty 10.4276 · 6,399,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dfcc23d8a3f53ed457bf450639ca9e72c4371294d5f8a69849c4ecd4918289b2

View on Chainz ↗

Height

#410,244

Difficulty

10.427614

Transactions

Size

2.25 KB

Version

Bits

0a6d781b

Nonce

9,241

Timestamp

2/18/2014, 10:41:24 PM

Confirmations

6,399,248

Mined by

⛏️ BaSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

9b07e9bbd4e1e6856ac81c9026275c11effcdb01d860dd3d6672cbdd1f5eaa98

Transactions (4)

Coinbase8bacc68eff5489…a757347033ed32

1 in → 20 out9.1800 XPM743 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 Ac7TsAMG…2W5MRTA8 Af76ewER…EzGhbQ6S

3d76a28653f514…eccdf0df20d8fd

5 in → 12 out38.8115 XPM1022 B

AYoWmPiG…7H5Kt86G AY4DoSD9…4yR8SYYf ASEHx7aD…63Kxp6r9 AVrD6maY…W77cdqzz AXpeLtme…E2zMsRT4

b71ae88150e720…035abc6f04faa1

1 in → 2 out6.0963 XPM226 B

ATbZoV5J…bdyt81P9 AHbJkDBK…5s7XmBbK

2b34d03c18eaa3…c6989620938856

1 in → 2 out4.9729 XPM225 B

AV7f78LJ…HGMpSq8z AVeRyAXB…51P2dFv5

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.

2.020 × 10⁹⁹(100-digit number)

20207173251699403605…36822370700318019679

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

2.020 × 10⁹⁹(100-digit number)

20207173251699403605…36822370700318019679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.020 × 10⁹⁹(100-digit number)

20207173251699403605…36822370700318019681

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

4.041 × 10⁹⁹(100-digit number)

40414346503398807210…73644741400636039359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.041 × 10⁹⁹(100-digit number)

40414346503398807210…73644741400636039361

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

8.082 × 10⁹⁹(100-digit number)

80828693006797614420…47289482801272078719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.082 × 10⁹⁹(100-digit number)

80828693006797614420…47289482801272078721

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

1.616 × 10¹⁰⁰(101-digit number)

16165738601359522884…94578965602544157439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.616 × 10¹⁰⁰(101-digit number)

16165738601359522884…94578965602544157441

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

3.233 × 10¹⁰⁰(101-digit number)

32331477202719045768…89157931205088314879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.233 × 10¹⁰⁰(101-digit number)

32331477202719045768…89157931205088314881

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 #410,244

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