Block #308,498

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/13/2013, 3:28:01 AM · Difficulty 9.9945 · 6,494,160 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a84c29e2a73fda99ed81918c429628860e18e93578c624cdf2c1799c897c4fb

View on Chainz ↗

Height

#308,498

Difficulty

9.994516

Transactions

Size

1.83 KB

Version

Bits

09fe9893

Nonce

9,852

Timestamp

12/13/2013, 3:28:01 AM

Confirmations

6,494,160

Mined by

⛏️ aRgAe6gEbs5i5LrBXcGb93Lduqktkm5Mn8oYw

Merkle Root

f7f75b5f70562aecbcc62c671afa46c00235b4530f321c57719f5c72a8d5c2d4

Transactions (4)

Coinbase2d8a4085cb733f…fcf45d64967f62

1 in → 22 out10.0000 XPM811 B

Ae6gEbs5…m5Mn8oYw Aac9Hjdg…P4ktypc3 ANNg88pG…ppn21sTe AGWYhPLV…1mrpnRmq AMPcXbqv…fK7wHymz

0d6dbf4db12510…b328a8fe00d5e4

3 in → 2 out5.9955 XPM520 B

APJxaqL2…fbdgVPYb AM1CYHUd…FJfpMDZv

545086a0d39eb9…b491c0ddb2b16c

1 in → 2 out72.7800 XPM227 B

AMWqj3pX…N5oYE5Nt AVvyhacf…VgfUiyaR

a854594f34b4b2…9b36dedaaeb908

1 in → 2 out6.4822 XPM226 B

AaWZJEh6…xg8gB5gZ AZTCSvMs…Cmo6RzTw

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.

7.992 × 10⁹²(93-digit number)

79929674393747511474…83977944713838525439

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

7.992 × 10⁹²(93-digit number)

79929674393747511474…83977944713838525439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.992 × 10⁹²(93-digit number)

79929674393747511474…83977944713838525441

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

1.598 × 10⁹³(94-digit number)

15985934878749502294…67955889427677050879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.598 × 10⁹³(94-digit number)

15985934878749502294…67955889427677050881

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

3.197 × 10⁹³(94-digit number)

31971869757499004589…35911778855354101759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.197 × 10⁹³(94-digit number)

31971869757499004589…35911778855354101761

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

6.394 × 10⁹³(94-digit number)

63943739514998009179…71823557710708203519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.394 × 10⁹³(94-digit number)

63943739514998009179…71823557710708203521

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

1.278 × 10⁹⁴(95-digit number)

12788747902999601835…43647115421416407039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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