Block #388,349

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/3/2014, 5:49:42 PM · Difficulty 10.4192 · 6,406,937 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

621183d8d67a60d1fa0e88ff2ef9247564cc69b1a5232afe00f75cbfdebdfcfa

View on Chainz ↗

Height

#388,349

Difficulty

10.419162

Transactions

Size

867 B

Version

Bits

0a6b4e32

Nonce

43,380

Timestamp

2/3/2014, 5:49:42 PM

Confirmations

6,406,937

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

af8422a69192cfcf931bf778f04c20f88c3cc47dbdc7237eb42c2cc50f1cfc5c

Transactions (1)

Coinbaseaf8422a69192cf…2c2cc50f1cfc5c

1 in → 21 out9.2000 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH AKzkYQaQ…zR4FspJZ

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.

8.355 × 10⁹³(94-digit number)

83553730057247749392…93764967140917356959

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

8.355 × 10⁹³(94-digit number)

83553730057247749392…93764967140917356959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.355 × 10⁹³(94-digit number)

83553730057247749392…93764967140917356961

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

1.671 × 10⁹⁴(95-digit number)

16710746011449549878…87529934281834713919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.671 × 10⁹⁴(95-digit number)

16710746011449549878…87529934281834713921

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

3.342 × 10⁹⁴(95-digit number)

33421492022899099756…75059868563669427839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.342 × 10⁹⁴(95-digit number)

33421492022899099756…75059868563669427841

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

6.684 × 10⁹⁴(95-digit number)

66842984045798199513…50119737127338855679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.684 × 10⁹⁴(95-digit number)

66842984045798199513…50119737127338855681

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

1.336 × 10⁹⁵(96-digit number)

13368596809159639902…00239474254677711359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.336 × 10⁹⁵(96-digit number)

13368596809159639902…00239474254677711361

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