Block #1,260,381

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/30/2015, 3:15:54 AM · Difficulty 10.8192 · 5,544,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0853e3bf0d10f39bfaa81bf765eb3c2e46e82d1c1e94eb40946ad303f681e146

View on Chainz ↗

Height

#1,260,381

Difficulty

10.819206

Transactions

Size

1.73 KB

Version

Bits

0ad1b775

Nonce

444,817,735

Timestamp

9/30/2015, 3:15:54 AM

Confirmations

5,544,552

Mined by

⛏️ P2SHAMJfaSoD2Ymugfd1MWU3WDzjqHimdL3nhe

Merkle Root

7bd97fd2eed2d3eab41a103738925a4e1aade714d0e55ee137b8fb5fb2970d90

Transactions (4)

Coinbased6f0759bfdbe80…4c2af384513d42

1 in → 1 out8.5600 XPM109 B

AMJfaSoD…imdL3nhe

c31238a8c5c23d…4ead383a06d78a

2 in → 2 out10.5454 XPM374 B

AbMeRh4h…e6PYFRf2 AeuV6ooX…wMxTFm1j

615e1da36ad274…f4cbf4f00acbd8

1 in → 2 out7.1069 XPM226 B

AepcE3U3…4gRuoe4g AQzGsiip…LXYjaGXj

525eb21785d139…e0fd1ee1d64346

6 in → 2 out1.0597 XPM967 B

ANfwhsyh…iYEHnbDU AeAhq3Hv…qd6WDiKe

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.

2.097 × 10⁹⁷(98-digit number)

20971812384219610398…19240828003498045439

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

2.097 × 10⁹⁷(98-digit number)

20971812384219610398…19240828003498045439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.097 × 10⁹⁷(98-digit number)

20971812384219610398…19240828003498045441

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

4.194 × 10⁹⁷(98-digit number)

41943624768439220797…38481656006996090879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.194 × 10⁹⁷(98-digit number)

41943624768439220797…38481656006996090881

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

8.388 × 10⁹⁷(98-digit number)

83887249536878441595…76963312013992181759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.388 × 10⁹⁷(98-digit number)

83887249536878441595…76963312013992181761

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

1.677 × 10⁹⁸(99-digit number)

16777449907375688319…53926624027984363519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.677 × 10⁹⁸(99-digit number)

16777449907375688319…53926624027984363521

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

3.355 × 10⁹⁸(99-digit number)

33554899814751376638…07853248055968727039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.355 × 10⁹⁸(99-digit number)

33554899814751376638…07853248055968727041

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