Block #1,419,104

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2016, 10:19:46 PM · Difficulty 10.7939 · 5,397,524 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2208319f068667c195197d0473bd8a04b11b6358c5bad02a72692f3b7a815ed

View on Chainz ↗

Height

#1,419,104

Difficulty

10.793941

Transactions

Size

867 B

Version

Bits

0acb3fb0

Nonce

764,366,793

Timestamp

1/18/2016, 10:19:46 PM

Confirmations

5,397,524

Mined by

⛏️ P2SHAeKDT3pU8wqD9znHchJFArggkXLtaD1QTq

Merkle Root

018e08091ecac9c378d09bc91ec8502bcf7a387f4c1ec939e7a12bec3a82ef6f

Transactions (2)

Coinbasef6c552b924f623…2ead01cf37ccb7

1 in → 1 out8.5800 XPM110 B

AeKDT3pU…LtaD1QTq

4ba6e270859fbb…99870d5fdb4952

1 in → 15 out34.7248 XPM667 B

ARGVY3Yg…qDWZXvfb AGsnZsNU…1zQrxoJz ARYdBu18…h9RLj24r AR1fsvgQ…d5WANr1D ARbmELZZ…D2EmA9eK

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.

2.684 × 10⁹⁴(95-digit number)

26845271513904984391…51015216032578452159

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

2.684 × 10⁹⁴(95-digit number)

26845271513904984391…51015216032578452159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.684 × 10⁹⁴(95-digit number)

26845271513904984391…51015216032578452161

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

5.369 × 10⁹⁴(95-digit number)

53690543027809968782…02030432065156904319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.369 × 10⁹⁴(95-digit number)

53690543027809968782…02030432065156904321

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

1.073 × 10⁹⁵(96-digit number)

10738108605561993756…04060864130313808639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.073 × 10⁹⁵(96-digit number)

10738108605561993756…04060864130313808641

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

2.147 × 10⁹⁵(96-digit number)

21476217211123987512…08121728260627617279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.147 × 10⁹⁵(96-digit number)

21476217211123987512…08121728260627617281

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

4.295 × 10⁹⁵(96-digit number)

42952434422247975025…16243456521255234559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.295 × 10⁹⁵(96-digit number)

42952434422247975025…16243456521255234561

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 #1,419,104

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