Block #309,155

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 11:22:12 AM · Difficulty 9.9947 · 6,507,705 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

91ad855ca77c9bcf97d757862c048880bb4691e0fa1da442971e114d60cadd48

View on Chainz ↗

Height

#309,155

Difficulty

9.994733

Transactions

Size

1002 B

Version

Bits

09fea6d4

Nonce

34,480

Timestamp

12/13/2013, 11:22:12 AM

Confirmations

6,507,705

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

dac20529a0393819f7e4de7c60dc0660ecadd908e9e18ff6335d94b623e63293

Transactions (1)

Coinbasedac20529a03938…5d94b623e63293

1 in → 25 out10.0000 XPM913 B

Aac9Hjdg…P4ktypc3 AHCbk3sT…ddhvYDDU AQM5Zq4c…Wu5TRqLn AUW89vJd…BiczGLRw Ad9pSzHt…cpJ3y2zz

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.

1.524 × 10⁹²(93-digit number)

15246173372405914470…64122678125141634559

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

1.524 × 10⁹²(93-digit number)

15246173372405914470…64122678125141634559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.524 × 10⁹²(93-digit number)

15246173372405914470…64122678125141634561

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

3.049 × 10⁹²(93-digit number)

30492346744811828940…28245356250283269119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.049 × 10⁹²(93-digit number)

30492346744811828940…28245356250283269121

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

6.098 × 10⁹²(93-digit number)

60984693489623657881…56490712500566538239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.098 × 10⁹²(93-digit number)

60984693489623657881…56490712500566538241

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

1.219 × 10⁹³(94-digit number)

12196938697924731576…12981425001133076479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.219 × 10⁹³(94-digit number)

12196938697924731576…12981425001133076481

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

2.439 × 10⁹³(94-digit number)

24393877395849463152…25962850002266152959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.439 × 10⁹³(94-digit number)

24393877395849463152…25962850002266152961

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 #309,155

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