Block #388,393

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2014, 6:33:29 PM · Difficulty 10.4192 · 6,419,344 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76474f72ac1a1cd6e6e2ab8cafa6e63042891a1931ad32bf03a6fe9d80f400a1

View on Chainz ↗

Height

#388,393

Difficulty

10.419200

Transactions

Size

1.10 KB

Version

Bits

0a6b50ac

Nonce

6,488

Timestamp

2/3/2014, 6:33:29 PM

Confirmations

6,419,344

Mined by

⛏️ -DAc2JYASPQD7vWBs42nkRqpCmFvtcBL5PEW

Merkle Root

aaa8ae45c0c64b980c5fae5061ed36dc84192fb88d4ce2cded22aa86ec69d021

Transactions (5)

Coinbase14f1531d173c22…bb436bd7a342e3

1 in → 2 out9.2400 XPM131 B

Ac2JYASP…tcBL5PEW AJno7LX2…vo4wdWtY

8677575336d4ce…d732ac2503a054

1 in → 2 out4.1019 XPM225 B

ANY2bMdV…bEQjn53S ARTVpFrz…DmqrU8Jb

379080aff7bd69…d089ecb471b0b0

1 in → 2 out4.1264 XPM225 B

AbTzGW73…sLHGYH1Q AGjuirjz…XLiqnXox

fcc0537df38610…a4e64555a47a3e

1 in → 2 out4.1272 XPM227 B

ALQx59LV…R8LoHHSH AGJcmGTu…8NpdazbJ

3b473029582eaf…e385de9318d614

1 in → 2 out1.3400 XPM227 B

Ac24WwPt…BSeTbxUj AJWkcEES…ducvCFZN

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.

1.805 × 10¹⁰⁰(101-digit number)

18055432814315405295…44548077555271585279

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

1.805 × 10¹⁰⁰(101-digit number)

18055432814315405295…44548077555271585279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.805 × 10¹⁰⁰(101-digit number)

18055432814315405295…44548077555271585281

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

3.611 × 10¹⁰⁰(101-digit number)

36110865628630810590…89096155110543170559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.611 × 10¹⁰⁰(101-digit number)

36110865628630810590…89096155110543170561

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

7.222 × 10¹⁰⁰(101-digit number)

72221731257261621181…78192310221086341119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.222 × 10¹⁰⁰(101-digit number)

72221731257261621181…78192310221086341121

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

1.444 × 10¹⁰¹(102-digit number)

14444346251452324236…56384620442172682239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.444 × 10¹⁰¹(102-digit number)

14444346251452324236…56384620442172682241

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

2.888 × 10¹⁰¹(102-digit number)

28888692502904648472…12769240884345364479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.888 × 10¹⁰¹(102-digit number)

28888692502904648472…12769240884345364481

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 #388,393

Cookie Preferences