Block #339,850

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 9:28:59 AM · Difficulty 10.1293 · 6,469,652 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

50b04fdf85f1bc5f0517f86de2d763570cbfe265ed22120f088a68fd4d388806

View on Chainz ↗

Height

#339,850

Difficulty

10.129320

Transactions

Size

1.05 KB

Version

Bits

0a211b1b

Nonce

110,047

Timestamp

1/2/2014, 9:28:59 AM

Confirmations

6,469,652

Mined by

⛏️ aR1AUAiwDbdd8GSUHgPrvFxFmFaRpdZRrtLWa

Merkle Root

acf585e6aa8d82ff05a69211ff83e9d53744541f924f0beb2d0808ed947f2552

Transactions (1)

Coinbaseacf585e6aa8d82…0808ed947f2552

1 in → 27 out9.7300 XPM981 B

AUAiwDbd…dZRrtLWa AGAf8Z9Q…ggDWo52w AQ8QAT3J…rCFKuVbR ALhUv7k5…gkaq7ePM AUH8MTP4…tSSjzeSq

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.

8.758 × 10⁹⁶(97-digit number)

87584158835852827205…70111150144648642559

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

8.758 × 10⁹⁶(97-digit number)

87584158835852827205…70111150144648642559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.758 × 10⁹⁶(97-digit number)

87584158835852827205…70111150144648642561

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

1.751 × 10⁹⁷(98-digit number)

17516831767170565441…40222300289297285119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.751 × 10⁹⁷(98-digit number)

17516831767170565441…40222300289297285121

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

3.503 × 10⁹⁷(98-digit number)

35033663534341130882…80444600578594570239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.503 × 10⁹⁷(98-digit number)

35033663534341130882…80444600578594570241

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

7.006 × 10⁹⁷(98-digit number)

70067327068682261764…60889201157189140479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.006 × 10⁹⁷(98-digit number)

70067327068682261764…60889201157189140481

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

1.401 × 10⁹⁸(99-digit number)

14013465413736452352…21778402314378280959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.401 × 10⁹⁸(99-digit number)

14013465413736452352…21778402314378280961

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 #339,850

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