Block #1,270,902

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/7/2015, 12:06:48 PM · Difficulty 10.8162 · 5,571,166 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ac3dfd99eb6510d4a77a1719606ee3747e6b64112b9b80e915fb14c834c7c05

View on Chainz ↗

Height

#1,270,902

Difficulty

10.816218

Transactions

Size

1.44 KB

Version

Bits

0ad0f3b0

Nonce

213,871,013

Timestamp

10/7/2015, 12:06:48 PM

Confirmations

5,571,166

Mined by

⛏️ P2SHAJCEY9yyy2DERzsA24UUtHTMGPtg97E6zm

Merkle Root

99388c9e7fe92a935a8e87c3f56040bfe000e68ba99fb461eca00f489e0a7594

Transactions (4)

Coinbasec47efe5819ff47…4804974046092d

1 in → 1 out8.5600 XPM116 B

AJCEY9yy…tg97E6zm

3fcc5e6c56a519…95b086784a0721

2 in → 2 out10.9422 XPM374 B

ALai2vyy…LSHBkNRP AdUwqsJC…kyCDagPM

574b2e92a9cead…0584e7bb7b2b4e

1 in → 15 out43.0995 XPM668 B

AHDZZNYt…AJpJgJfM AVM3B4py…gzRoNnok AdXaUrde…ZoizVcpy AbUgRDkj…RPTqufBa AG8LSuD4…MWdCU2HR

cfd1fc37242a2d…6b77e9619ed013

1 in → 2 out7.4530 XPM227 B

AbBbCuqG…ZNc9ysbR AcuM7XiJ…5uND8Jce

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.

2.400 × 10⁹⁷(98-digit number)

24004517610079301578…21396767326849761279

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

2.400 × 10⁹⁷(98-digit number)

24004517610079301578…21396767326849761279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.400 × 10⁹⁷(98-digit number)

24004517610079301578…21396767326849761281

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

4.800 × 10⁹⁷(98-digit number)

48009035220158603157…42793534653699522559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.800 × 10⁹⁷(98-digit number)

48009035220158603157…42793534653699522561

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

9.601 × 10⁹⁷(98-digit number)

96018070440317206314…85587069307399045119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.601 × 10⁹⁷(98-digit number)

96018070440317206314…85587069307399045121

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

1.920 × 10⁹⁸(99-digit number)

19203614088063441262…71174138614798090239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.920 × 10⁹⁸(99-digit number)

19203614088063441262…71174138614798090241

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

3.840 × 10⁹⁸(99-digit number)

38407228176126882525…42348277229596180479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.840 × 10⁹⁸(99-digit number)

38407228176126882525…42348277229596180481

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 #1,270,902

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