Block #3,508,897

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/11/2020, 2:48:26 AM · Difficulty 10.9289 · 3,334,366 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5256eb89a99ca5f3b90cce6969408db49de925ed73ae08b920fccc6659861d12

View on Chainz ↗

Height

#3,508,897

Difficulty

10.928944

Transactions

Size

3.55 KB

Version

Bits

0aedcf42

Nonce

1,649,224,107

Timestamp

1/11/2020, 2:48:26 AM

Confirmations

3,334,366

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

351153469c230005930d9becdb2993a12825ed5b0f20bbfe69b53d57156a2a5c

Transactions (5)

Coinbaseb1912141b83ce6…14076b41889fe8

1 in → 1 out8.4100 XPM110 B

ASiq2qtK…VMhmk7yL

8bfad52799f804…68dc20b649b406

3 in → 2 out25.0900 XPM421 B

AXMsS7rS…QVJwPNhf ASiq2qtK…VMhmk7yL

fcd991f9258995…9bdd2aa0eba029

15 in → 2 out100.0967 XPM1.88 KB

Ab5fFXVt…EC9k8a2d ASiq2qtK…VMhmk7yL

b55a0c4d20caaf…12fa2b5798f1f2

3 in → 2 out21.0116 XPM454 B

AFnJw5W4…kv14VDme ASiq2qtK…VMhmk7yL

4cf98e2f65559c…93390dd24ad92d

4 in → 2 out10.0523 XPM637 B

ASiq2qtK…VMhmk7yL AZML7PkD…gCPLTjtA

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.

1.759 × 10⁹³(94-digit number)

17596924086002283318…47270023126643657889

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

1.759 × 10⁹³(94-digit number)

17596924086002283318…47270023126643657889

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.759 × 10⁹³(94-digit number)

17596924086002283318…47270023126643657891

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

3.519 × 10⁹³(94-digit number)

35193848172004566636…94540046253287315779

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.519 × 10⁹³(94-digit number)

35193848172004566636…94540046253287315781

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

7.038 × 10⁹³(94-digit number)

70387696344009133272…89080092506574631559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.038 × 10⁹³(94-digit number)

70387696344009133272…89080092506574631561

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

1.407 × 10⁹⁴(95-digit number)

14077539268801826654…78160185013149263119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.407 × 10⁹⁴(95-digit number)

14077539268801826654…78160185013149263121

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

2.815 × 10⁹⁴(95-digit number)

28155078537603653308…56320370026298526239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.815 × 10⁹⁴(95-digit number)

28155078537603653308…56320370026298526241

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 #3,508,897

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