Block #2,163,782

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/17/2017, 12:00:31 AM · Difficulty 10.8995 · 4,679,354 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16bc7d18d5bc5b36fe2340be65250aee79186b5adc08c3571b3007cd8cf47f9f

View on Chainz ↗

Height

#2,163,782

Difficulty

10.899492

Transactions

Size

1.08 KB

Version

Bits

0ae64514

Nonce

291,638,657

Timestamp

6/17/2017, 12:00:31 AM

Confirmations

4,679,354

Mined by

⛏️ P2SHAWMrzWMKcHJkN1TbD1uvATBPjFtoDjNSww

Merkle Root

8ef82efbf8b2a50e49d930b211f361bda81b94a989b383e2f08fa66edf680e3a

Transactions (5)

Coinbasebb7e72c4c85e96…e3054ff34a3893

1 in → 1 out8.4400 XPM109 B

AWMrzWMK…toDjNSww

a335306ce3cca2…dd40e7de8a8d3f

1 in → 2 out4.3800 XPM226 B

Ac8vep5P…Lbovnxyc AVLyDRTf…iGHrtE3z

c1f5d64160fe0f…3786c1b7e8bed4

1 in → 2 out4.3800 XPM226 B

AcdjojGR…MgZamZJZ Ae7aFiaF…4GMb3LpH

5e8eded2557739…7da8455bc52495

1 in → 2 out4.3800 XPM226 B

AaHBuqne…B82zEjwZ ANNDg4rt…pAzHwCrJ

30dd8042ada101…48884abc5f3057

1 in → 2 out4.3800 XPM226 B

AXiTmxAE…HFKkv3Dr ANEMMbxx…yxibpPYi

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.

2.898 × 10⁹⁵(96-digit number)

28987747361554395817…61843425420677734399

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

2.898 × 10⁹⁵(96-digit number)

28987747361554395817…61843425420677734399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.898 × 10⁹⁵(96-digit number)

28987747361554395817…61843425420677734401

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

5.797 × 10⁹⁵(96-digit number)

57975494723108791634…23686850841355468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.797 × 10⁹⁵(96-digit number)

57975494723108791634…23686850841355468801

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

1.159 × 10⁹⁶(97-digit number)

11595098944621758326…47373701682710937599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.159 × 10⁹⁶(97-digit number)

11595098944621758326…47373701682710937601

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

2.319 × 10⁹⁶(97-digit number)

23190197889243516653…94747403365421875199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.319 × 10⁹⁶(97-digit number)

23190197889243516653…94747403365421875201

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

4.638 × 10⁹⁶(97-digit number)

46380395778487033307…89494806730843750399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.638 × 10⁹⁶(97-digit number)

46380395778487033307…89494806730843750401

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 #2,163,782

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