Block #935,202

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2015, 9:41:21 PM · Difficulty 10.9015 · 5,871,170 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

962aaa6b4ad7098ca20419cea19c66e929064a3af439b6a87bd3fb98aeaa138f

View on Chainz ↗

Height

#935,202

Difficulty

10.901451

Transactions

Size

999 B

Version

Bits

0ae6c579

Nonce

583,905,246

Timestamp

2/13/2015, 9:41:21 PM

Confirmations

5,871,170

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

965b5e5c12320cc648da1da5fe3926cbab60a577761debd36adb0531642bfc37

Transactions (4)

Coinbase140ca021f938f8…6c13c8f34f5d52

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

ce4688f4a2a6e1…3698eba70c14ac

2 in → 1 out10.1230 XPM341 B

AWF4rtPp…LnbQHVaN

7e2c96f704aa75…805c07f2905273

1 in → 2 out6.7420 XPM226 B

AHRoBSh4…BSVTQ36Q ANbCBnUM…sicXmAqq

4a87f22e5a3360…6fa456ff7bfd2f

1 in → 2 out3.2852 XPM226 B

AdWEcK3r…HNaeWgVb AZhW7Cm3…uPxzUhXV

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.

1.333 × 10⁹⁵(96-digit number)

13330714775821387443…51682975958709249699

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

1.333 × 10⁹⁵(96-digit number)

13330714775821387443…51682975958709249699

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.333 × 10⁹⁵(96-digit number)

13330714775821387443…51682975958709249701

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

2.666 × 10⁹⁵(96-digit number)

26661429551642774887…03365951917418499399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.666 × 10⁹⁵(96-digit number)

26661429551642774887…03365951917418499401

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

5.332 × 10⁹⁵(96-digit number)

53322859103285549774…06731903834836998799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.332 × 10⁹⁵(96-digit number)

53322859103285549774…06731903834836998801

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

1.066 × 10⁹⁶(97-digit number)

10664571820657109954…13463807669673997599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.066 × 10⁹⁶(97-digit number)

10664571820657109954…13463807669673997601

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

2.132 × 10⁹⁶(97-digit number)

21329143641314219909…26927615339347995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.132 × 10⁹⁶(97-digit number)

21329143641314219909…26927615339347995201

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 #935,202

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