Block #1,312,216

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/4/2015, 11:03:28 AM · Difficulty 10.8523 · 5,513,443 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e9be3a925935d675ec41761792c2d1851c6fb10438fc8d391e8b12d97944257

View on Chainz ↗

Height

#1,312,216

Difficulty

10.852312

Transactions

Size

1.05 KB

Version

Bits

0ada3120

Nonce

1,161,107,502

Timestamp

11/4/2015, 11:03:28 AM

Confirmations

5,513,443

Mined by

⛏️ P2SHAG9CBKn1ye8GxT8jySagWrVzegdjm2ThGD

Merkle Root

00db6fa3f9800a13a61c0b7cf8ae100235088051efe2f22ba46a66a7766d9121

Transactions (2)

Coinbase91eeab3f0e8c34…c7a30ecaf2c120

1 in → 1 out8.4900 XPM110 B

AG9CBKn1…djm2ThGD

eaa7cbc8ac4fd9…b3904441526f00

1 in → 21 out184.6603 XPM871 B

APN4FKyi…TCbsy71F AL6hvktR…nkuNSDvK AGKBJSee…efFppq6o Abr1BP78…7dmG3fFa Af77jyrG…wM9SsxLZ

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.

3.448 × 10⁹⁵(96-digit number)

34489032450881176969…71966585012884423679

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

3.448 × 10⁹⁵(96-digit number)

34489032450881176969…71966585012884423679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.448 × 10⁹⁵(96-digit number)

34489032450881176969…71966585012884423681

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

6.897 × 10⁹⁵(96-digit number)

68978064901762353939…43933170025768847359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.897 × 10⁹⁵(96-digit number)

68978064901762353939…43933170025768847361

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

1.379 × 10⁹⁶(97-digit number)

13795612980352470787…87866340051537694719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.379 × 10⁹⁶(97-digit number)

13795612980352470787…87866340051537694721

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

2.759 × 10⁹⁶(97-digit number)

27591225960704941575…75732680103075389439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.759 × 10⁹⁶(97-digit number)

27591225960704941575…75732680103075389441

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

5.518 × 10⁹⁶(97-digit number)

55182451921409883151…51465360206150778879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.518 × 10⁹⁶(97-digit number)

55182451921409883151…51465360206150778881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.103 × 10⁹⁷(98-digit number)

11036490384281976630…02930720412301557759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,312,216

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