Block #387,499

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2014, 4:35:22 AM · Difficulty 10.4125 · 6,422,295 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e372edf4d89721d3fc6818e4bdaf2490a374afdd497b35600e819456053dd7b8

View on Chainz ↗

Height

#387,499

Difficulty

10.412477

Transactions

Size

1.11 KB

Version

Bits

0a699820

Nonce

46,330

Timestamp

2/3/2014, 4:35:22 AM

Confirmations

6,422,295

Mined by

⛏️ aR|JAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

20b959c8a3b0c54073e9d1fd063c1f3aca14f8961f33ba47688e2b4472061ff5

Transactions (2)

Coinbase8d9106a26d388b…7813cf82ecc097

1 in → 19 out9.2048 XPM709 B

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

5c39773088c42b…0d2b256f0e6379

2 in → 1 out5.9974 XPM339 B

ARAW88nM…Xp5D5rie

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.

1.919 × 10⁹⁷(98-digit number)

19192454407078827079…21438048445595818239

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

1.919 × 10⁹⁷(98-digit number)

19192454407078827079…21438048445595818239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.919 × 10⁹⁷(98-digit number)

19192454407078827079…21438048445595818241

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

3.838 × 10⁹⁷(98-digit number)

38384908814157654158…42876096891191636479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.838 × 10⁹⁷(98-digit number)

38384908814157654158…42876096891191636481

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

7.676 × 10⁹⁷(98-digit number)

76769817628315308316…85752193782383272959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.676 × 10⁹⁷(98-digit number)

76769817628315308316…85752193782383272961

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

1.535 × 10⁹⁸(99-digit number)

15353963525663061663…71504387564766545919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.535 × 10⁹⁸(99-digit number)

15353963525663061663…71504387564766545921

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

3.070 × 10⁹⁸(99-digit number)

30707927051326123326…43008775129533091839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.070 × 10⁹⁸(99-digit number)

30707927051326123326…43008775129533091841

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 #387,499

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