Block #935,632

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/14/2015, 5:21:43 AM · Difficulty 10.9009 · 5,878,299 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

079c7e6172bd2db0bd5a1256b0e82e90964e8cd3137245fe641b3a4bbb0a5c60

View on Chainz ↗

Height

#935,632

Difficulty

10.900896

Transactions

Size

1.01 KB

Version

Bits

0ae6a11f

Nonce

571,895,465

Timestamp

2/14/2015, 5:21:43 AM

Confirmations

5,878,299

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

35996242f90be5971c0b3665899b629cf59669740748b99a50c8e1ef1efb03ad

Transactions (4)

Coinbasee1a0cba2455c97…2ceb8be57b7473

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

c00436316cb062…00b69f33ff44e1

2 in → 2 out13.9213 XPM375 B

ATDzT9Qg…xPgwgjb1 AbKwuVVV…oGGhe36W

0f4820f4d9f194…05c039f623ee47

1 in → 2 out6.7000 XPM227 B

AcbChLEZ…AEgQmQpd AHRoBSh4…BSVTQ36Q

e72129e58240dd…e81181e178328e

1 in → 2 out3.8904 XPM227 B

AVZwze3C…1DNKwKx6 AHpxw8Cz…78MatZgX

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.

3.795 × 10⁹⁶(97-digit number)

37950036452182757815…46168202807418519999

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

3.795 × 10⁹⁶(97-digit number)

37950036452182757815…46168202807418519999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.795 × 10⁹⁶(97-digit number)

37950036452182757815…46168202807418520001

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

7.590 × 10⁹⁶(97-digit number)

75900072904365515631…92336405614837039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.590 × 10⁹⁶(97-digit number)

75900072904365515631…92336405614837040001

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

1.518 × 10⁹⁷(98-digit number)

15180014580873103126…84672811229674079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.518 × 10⁹⁷(98-digit number)

15180014580873103126…84672811229674080001

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

3.036 × 10⁹⁷(98-digit number)

30360029161746206252…69345622459348159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.036 × 10⁹⁷(98-digit number)

30360029161746206252…69345622459348160001

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

6.072 × 10⁹⁷(98-digit number)

60720058323492412505…38691244918696319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.072 × 10⁹⁷(98-digit number)

60720058323492412505…38691244918696320001

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

1.214 × 10⁹⁸(99-digit number)

12144011664698482501…77382489837392639999

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 #935,632

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