Block #393,331

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/7/2014, 2:42:11 AM · Difficulty 10.4355 · 6,412,929 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4c2890f0df96d15a6b4d38cb2265aa762963571dae3a3821909b80248e075b5

View on Chainz ↗

Height

#393,331

Difficulty

10.435462

Transactions

Size

1.58 KB

Version

Bits

0a6f7a74

Nonce

88,719

Timestamp

2/7/2014, 2:42:11 AM

Confirmations

6,412,929

Mined by

⛏️ saRGAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

14bb93d6bfadf5bbaefcd9ff9cdf9212198a47d21ce46adf231669d14ee206e1

Transactions (4)

Coinbase7fafa89891ecb5…8475174a3b1615

1 in → 23 out9.1700 XPM845 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6

d9bd41fb1ec84e…937ef3eeebdbcf

1 in → 2 out15371.6499 XPM225 B

AWsznUCk…QjtRoTFB AS9KkyEi…PuULcPms

9c8721a7a37890…271e090ce49796

1 in → 2 out6.9822 XPM227 B

AK5QFPz5…ywR3aKST AcDdg3hs…vRTBLoEV

c9b8783900684a…db7cf8ad59ce13

1 in → 2 out5.1487 XPM226 B

AKffMzGk…FN7PTReu ALHbRxMJ…LEi9pifp

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.

1.314 × 10⁹⁴(95-digit number)

13147336973091070182…41338118280004041279

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

1.314 × 10⁹⁴(95-digit number)

13147336973091070182…41338118280004041279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.314 × 10⁹⁴(95-digit number)

13147336973091070182…41338118280004041281

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

2.629 × 10⁹⁴(95-digit number)

26294673946182140365…82676236560008082559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.629 × 10⁹⁴(95-digit number)

26294673946182140365…82676236560008082561

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

5.258 × 10⁹⁴(95-digit number)

52589347892364280730…65352473120016165119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.258 × 10⁹⁴(95-digit number)

52589347892364280730…65352473120016165121

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

1.051 × 10⁹⁵(96-digit number)

10517869578472856146…30704946240032330239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.051 × 10⁹⁵(96-digit number)

10517869578472856146…30704946240032330241

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

2.103 × 10⁹⁵(96-digit number)

21035739156945712292…61409892480064660479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.103 × 10⁹⁵(96-digit number)

21035739156945712292…61409892480064660481

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 #393,331

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