Block #309,882

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 7:37:43 PM · Difficulty 9.9950 · 6,517,108 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99d4c654cc13e8822f1c7c0d23f5bfdd9ed2cef729cd74e4f6cf5b86110dd6ff

View on Chainz ↗

Height

#309,882

Difficulty

9.994991

Transactions

Size

1.08 KB

Version

Bits

09feb7b7

Nonce

179,793

Timestamp

12/13/2013, 7:37:43 PM

Confirmations

6,517,108

Mined by

⛏️ zaRa&AYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

b7fbfbf4cef0b10d8490fb1fff05ef72e5958e88e2f1832c2a8cb0df3d006609

Transactions (1)

Coinbaseb7fbfbf4cef0b1…8cb0df3d006609

1 in → 28 out9.9728 XPM1015 B

AYtDvcGs…VuAcA7m7 AYcLTeXR…bscgPops Aac9Hjdg…P4ktypc3 Ad9pSzHt…cpJ3y2zz ALaSmG93…4TA3uNAR

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.

1.281 × 10⁹⁶(97-digit number)

12818390633500758924…52896183775552817199

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

1.281 × 10⁹⁶(97-digit number)

12818390633500758924…52896183775552817199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.281 × 10⁹⁶(97-digit number)

12818390633500758924…52896183775552817201

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

2.563 × 10⁹⁶(97-digit number)

25636781267001517849…05792367551105634399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.563 × 10⁹⁶(97-digit number)

25636781267001517849…05792367551105634401

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

5.127 × 10⁹⁶(97-digit number)

51273562534003035698…11584735102211268799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.127 × 10⁹⁶(97-digit number)

51273562534003035698…11584735102211268801

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

1.025 × 10⁹⁷(98-digit number)

10254712506800607139…23169470204422537599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.025 × 10⁹⁷(98-digit number)

10254712506800607139…23169470204422537601

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

2.050 × 10⁹⁷(98-digit number)

20509425013601214279…46338940408845075199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.050 × 10⁹⁷(98-digit number)

20509425013601214279…46338940408845075201

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 #309,882

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