Block #302,372

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 6:56:16 PM · Difficulty 9.9927 · 6,490,373 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1ab1cebc32757f91cf7c61a4a745dd65c5cfcbf2078a7c7acc1acaec83750b9

View on Chainz ↗

Height

#302,372

Difficulty

9.992688

Transactions

Size

1.22 KB

Version

Bits

09fe20d0

Nonce

7,425

Timestamp

12/9/2013, 6:56:16 PM

Confirmations

6,490,373

Merkle Root

da41b0eec2201a03bce016e13c352ac3433f4e0f12bc41924d2be25c0747245d

Transactions (3)

Coinbase80ab7033a7e3af…fe7e590139c583

1 in → 2 out10.0200 XPM141 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

055ad102761f94…b7c5486b045e75

1 in → 2 out16.6333 XPM226 B

ALrgGiZS…XxJjngCT AVxRAFUd…ivfKAeZQ

a79088fe2ee2f8…64a3cc1ee2b3bc

5 in → 1 out15.1400 XPM785 B

AMBC6JGb…tZMXhMBC

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.

1.969 × 10¹⁰⁵(106-digit number)

19696959125172928519…20530212560487423999

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

1.969 × 10¹⁰⁵(106-digit number)

19696959125172928519…20530212560487423999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.969 × 10¹⁰⁵(106-digit number)

19696959125172928519…20530212560487424001

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

3.939 × 10¹⁰⁵(106-digit number)

39393918250345857039…41060425120974847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.939 × 10¹⁰⁵(106-digit number)

39393918250345857039…41060425120974848001

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

7.878 × 10¹⁰⁵(106-digit number)

78787836500691714078…82120850241949695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.878 × 10¹⁰⁵(106-digit number)

78787836500691714078…82120850241949696001

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

1.575 × 10¹⁰⁶(107-digit number)

15757567300138342815…64241700483899391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.575 × 10¹⁰⁶(107-digit number)

15757567300138342815…64241700483899392001

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

3.151 × 10¹⁰⁶(107-digit number)

31515134600276685631…28483400967798783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.151 × 10¹⁰⁶(107-digit number)

31515134600276685631…28483400967798784001

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