Block #908,935

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/25/2015, 4:38:51 AM · Difficulty 10.9345 · 5,902,125 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a5fbd5cf8ea1c202ce7bc6fee4c72cee4a900f61042ee792cebd3b007528c172

View on Chainz ↗

Height

#908,935

Difficulty

10.934484

Transactions

Size

730 B

Version

Bits

0aef3a5a

Nonce

1,979,782,109

Timestamp

1/25/2015, 4:38:51 AM

Confirmations

5,902,125

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

01fef3570c0effee8fbb3ef0ee8c77ce15618019166d031d0b55b9e84c51af5b

Transactions (2)

Coinbase447c05b24db117…ad1204e6696c59

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

0a1993c4d9b04d…efe231b298ced1

3 in → 2 out105.4924 XPM523 B

AYgVgCwa…dQ7pvHnw AYbQUuPy…ngBocWSr

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.

1.041 × 10⁹⁶(97-digit number)

10419295998227018089…82926422529652862399

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

1.041 × 10⁹⁶(97-digit number)

10419295998227018089…82926422529652862399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.041 × 10⁹⁶(97-digit number)

10419295998227018089…82926422529652862401

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

2.083 × 10⁹⁶(97-digit number)

20838591996454036178…65852845059305724799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.083 × 10⁹⁶(97-digit number)

20838591996454036178…65852845059305724801

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

4.167 × 10⁹⁶(97-digit number)

41677183992908072357…31705690118611449599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.167 × 10⁹⁶(97-digit number)

41677183992908072357…31705690118611449601

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

8.335 × 10⁹⁶(97-digit number)

83354367985816144715…63411380237222899199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.335 × 10⁹⁶(97-digit number)

83354367985816144715…63411380237222899201

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

1.667 × 10⁹⁷(98-digit number)

16670873597163228943…26822760474445798399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.667 × 10⁹⁷(98-digit number)

16670873597163228943…26822760474445798401

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

3.334 × 10⁹⁷(98-digit number)

33341747194326457886…53645520948891596799

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 #908,935

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