Block #1,272,486

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/8/2015, 12:07:16 PM · Difficulty 10.8214 · 5,523,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8525a0c783b0c8dfd61fbaf95ec48b6bd7ecfbbdf3462fce3bdda001083f29f7

View on Chainz ↗

Height

#1,272,486

Difficulty

10.821419

Transactions

Size

1023 B

Version

Bits

0ad24880

Nonce

202,097,479

Timestamp

10/8/2015, 12:07:16 PM

Confirmations

5,523,426

Mined by

⛏️ P2SHAcppcwfuKgv4ZKmrQ2GiTMpNoM6iaqEM5D

Merkle Root

57e5eaf986b521554f382e1649d01b5e287233d09433bc2c632ddde8d9f9ebe5

Transactions (4)

Coinbasef15b9e80927782…0c2768f40ed736

1 in → 1 out8.5600 XPM109 B

Acppcwfu…6iaqEM5D

dbc54dbed88200…f3361c3148e7c0

1 in → 2 out8.5100 XPM227 B

AewXgmdm…HvDKRDE6 Aa4PtTwK…H3ppZFzk

8785b6ba413941…339c37a8d81773

1 in → 2 out8.5100 XPM225 B

AcuM7XiJ…5uND8Jce AdARTX2N…ytZ3i7GX

0121148e9326b7…0eb5dae81229da

2 in → 2 out13.6804 XPM372 B

Abf86izC…hKnEAsZ8 AJRwGPSP…QDRWdi2B

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.

7.629 × 10⁹³(94-digit number)

76298594733133930478…19237669849868342469

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

7.629 × 10⁹³(94-digit number)

76298594733133930478…19237669849868342469

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.629 × 10⁹³(94-digit number)

76298594733133930478…19237669849868342471

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

1.525 × 10⁹⁴(95-digit number)

15259718946626786095…38475339699736684939

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.525 × 10⁹⁴(95-digit number)

15259718946626786095…38475339699736684941

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

3.051 × 10⁹⁴(95-digit number)

30519437893253572191…76950679399473369879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.051 × 10⁹⁴(95-digit number)

30519437893253572191…76950679399473369881

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

6.103 × 10⁹⁴(95-digit number)

61038875786507144383…53901358798946739759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.103 × 10⁹⁴(95-digit number)

61038875786507144383…53901358798946739761

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

1.220 × 10⁹⁵(96-digit number)

12207775157301428876…07802717597893479519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.220 × 10⁹⁵(96-digit number)

12207775157301428876…07802717597893479521

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