Block #1,041,234

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2015, 4:59:41 AM · Difficulty 10.7258 · 5,772,787 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67789e0ebeb4119b4ba79c82ba57629023088c32e73a0268210f10d2602d4371

View on Chainz ↗

Height

#1,041,234

Difficulty

10.725754

Transactions

Size

4.34 KB

Version

Bits

0ab9caff

Nonce

357,271,474

Timestamp

5/2/2015, 4:59:41 AM

Confirmations

5,772,787

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

61f1f301eb19579c12ac45a2eabdd82761dd5845b0ac1b01de1dded5384b83b5

Transactions (5)

Coinbase180dc3fcfe15ed…e0a122ccbd7ca2

1 in → 1 out8.7400 XPM116 B

ANSXnLY2…Sd25TjkD

f9271a5a9e5fe8…df3b2c06619a09

1 in → 2 out8.5700 XPM226 B

AN2mfj8Z…yKQrT35w AKKnFqop…xxu5XWDy

b18c99f1113078…5f00d112d5c4b7

1 in → 51 out80.3200 XPM1.85 KB

ASG21nzq…iMYaGLq3 AWfTyjtG…6wHPHg62 AbGkyBKw…fE17qKkd AT9xtyNf…KvkLtFbk AVHU246Y…XCoEXEwP

518274dc85fb17…6362c881d26fa3

1 in → 51 out46.2460 XPM1.85 KB

ARbmELZZ…D2EmA9eK AQNJEZtc…oZUdvLf3 AJBLPVjE…EVWPWSBG AMHZxgto…dJWKiiFy APM3RoGj…Vb6frVuB

f93e77de6b3829…e009856a86b161

1 in → 2 out2.7746 XPM227 B

AQ6e6boQ…eqJoyqa8 Af3aPj7K…cnGd5dnY

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.

4.540 × 10⁹⁹(100-digit number)

45400557692879187291…48517613584142827519

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

4.540 × 10⁹⁹(100-digit number)

45400557692879187291…48517613584142827519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.540 × 10⁹⁹(100-digit number)

45400557692879187291…48517613584142827521

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

9.080 × 10⁹⁹(100-digit number)

90801115385758374583…97035227168285655039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.080 × 10⁹⁹(100-digit number)

90801115385758374583…97035227168285655041

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

1.816 × 10¹⁰⁰(101-digit number)

18160223077151674916…94070454336571310079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.816 × 10¹⁰⁰(101-digit number)

18160223077151674916…94070454336571310081

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

3.632 × 10¹⁰⁰(101-digit number)

36320446154303349833…88140908673142620159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.632 × 10¹⁰⁰(101-digit number)

36320446154303349833…88140908673142620161

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

7.264 × 10¹⁰⁰(101-digit number)

72640892308606699667…76281817346285240319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.264 × 10¹⁰⁰(101-digit number)

72640892308606699667…76281817346285240321

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 #1,041,234

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