Block #3,448,214

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/25/2019, 10:57:07 AM · Difficulty 10.9791 · 3,391,923 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

273d31d726863bf84623627eaafb4a917c9a5b4fc5474c8b9708ddb4a40ae307

View on Chainz ↗

Height

#3,448,214

Difficulty

10.979096

Transactions

Size

2.98 KB

Version

Bits

0afaa611

Nonce

70,453,462

Timestamp

11/25/2019, 10:57:07 AM

Confirmations

3,391,923

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

84f9ce6e5fff6f18e38479b4f27a0da0a0b95592c1b77e07520c0986616af05c

Transactions (2)

Coinbase4000d01e7bb1e3…f21a70ad219a0d

1 in → 1 out8.3100 XPM110 B

ASiq2qtK…VMhmk7yL

3bb0d431ef805f…ac13e46d29d3f9

19 in → 1 out190.7765 XPM2.78 KB

AXoSyMCe…Z8KXiWkn

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.

2.343 × 10⁹⁹(100-digit number)

23437430233762003303…95343550062453063679

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

2.343 × 10⁹⁹(100-digit number)

23437430233762003303…95343550062453063679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.343 × 10⁹⁹(100-digit number)

23437430233762003303…95343550062453063681

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

4.687 × 10⁹⁹(100-digit number)

46874860467524006606…90687100124906127359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.687 × 10⁹⁹(100-digit number)

46874860467524006606…90687100124906127361

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

9.374 × 10⁹⁹(100-digit number)

93749720935048013212…81374200249812254719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.374 × 10⁹⁹(100-digit number)

93749720935048013212…81374200249812254721

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

1.874 × 10¹⁰⁰(101-digit number)

18749944187009602642…62748400499624509439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.874 × 10¹⁰⁰(101-digit number)

18749944187009602642…62748400499624509441

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

3.749 × 10¹⁰⁰(101-digit number)

37499888374019205284…25496800999249018879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.749 × 10¹⁰⁰(101-digit number)

37499888374019205284…25496800999249018881

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

7.499 × 10¹⁰⁰(101-digit number)

74999776748038410569…50993601998498037759

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 #3,448,214

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