Block #1,654,065

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/30/2016, 1:53:20 PM · Difficulty 10.7708 · 5,162,814 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

66045c6690b50fb9a73a5b1d80a3d499bb9532b57314ce2b0d046714e2f2cd82

View on Chainz ↗

Height

#1,654,065

Difficulty

10.770762

Transactions

Size

21.22 KB

Version

Bits

0ac550ac

Nonce

168,838,413

Timestamp

6/30/2016, 1:53:20 PM

Confirmations

5,162,814

Mined by

⛏️ P2SHAXvCPra2YtAckUhLot9C1vGdGZgxC9AbLb

Merkle Root

53505f3c5b2da1da3fa6f75996576bc53fd97d25aacd40c1fd4171c6a21038e3

Transactions (2)

Coinbase4dde118b689215…be7528ce7d6dec

1 in → 1 out8.9900 XPM110 B

AXvCPra2…gxC9AbLb

aa341360c61279…9421d72f8410fd

145 in → 2 out64.0099 XPM21.02 KB

ASLB2zLr…KbeXUEoA AV9GdgNB…V4F2yhNU

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.

1.684 × 10⁹⁵(96-digit number)

16845154323908493519…62247087986620819839

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

1.684 × 10⁹⁵(96-digit number)

16845154323908493519…62247087986620819839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.684 × 10⁹⁵(96-digit number)

16845154323908493519…62247087986620819841

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

3.369 × 10⁹⁵(96-digit number)

33690308647816987038…24494175973241639679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.369 × 10⁹⁵(96-digit number)

33690308647816987038…24494175973241639681

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

6.738 × 10⁹⁵(96-digit number)

67380617295633974076…48988351946483279359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.738 × 10⁹⁵(96-digit number)

67380617295633974076…48988351946483279361

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

1.347 × 10⁹⁶(97-digit number)

13476123459126794815…97976703892966558719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.347 × 10⁹⁶(97-digit number)

13476123459126794815…97976703892966558721

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

2.695 × 10⁹⁶(97-digit number)

26952246918253589630…95953407785933117439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.695 × 10⁹⁶(97-digit number)

26952246918253589630…95953407785933117441

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 #1,654,065

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