Block #299,201

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 7:49:39 PM · Difficulty 9.9921 · 6,495,342 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

48f94991101c4e4f5af7d6dd0c5b20f2683bbc75c806157a64ace03e2d639cd0

View on Chainz ↗

Height

#299,201

Difficulty

9.992066

Transactions

Size

2.10 KB

Version

Bits

09fdf810

Nonce

170,494

Timestamp

12/7/2013, 7:49:39 PM

Confirmations

6,495,342

Mined by

⛏️ aR{Ad9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

9942fd324b40eca245fa9ba9967f6bf76b1cb42172be544135bf149540b38942

Transactions (4)

Coinbase1452cad6638bf1…13f2cdd9e18de9

1 in → 28 out9.9800 XPM1015 B

Ad9pSzHt…cpJ3y2zz AYtDvcGs…VuAcA7m7 AHuJ9wYh…BGmgHrKZ AWXYBWKP…qQAoisBJ AN63YyQR…1tfe566A

e340dc91a7782e…f709ad81e02459

3 in → 7 out20.1661 XPM625 B

ARqv8Lwm…Jt2HBwKy AeKNrjNj…1NEq95Ta AcEfJLzo…Ly8aDU8m AcxWR4Wm…zKQEbeG7 ANTGMD8n…pvc8NoeL

7abbb47cc6c5cb…11e4e63a5db10d

1 in → 2 out1475.1005 XPM226 B

AMWhfZow…EH5vsb34 AMK1rtnH…U7qBuYQk

de7b82ed50e1a5…9bd198c4ad7525

1 in → 1 out3.0077 XPM192 B

AdrVFPwD…WbnMHNBa

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.

6.495 × 10⁹⁷(98-digit number)

64953239058791350514…62029950020023847999

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

6.495 × 10⁹⁷(98-digit number)

64953239058791350514…62029950020023847999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.495 × 10⁹⁷(98-digit number)

64953239058791350514…62029950020023848001

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

1.299 × 10⁹⁸(99-digit number)

12990647811758270102…24059900040047695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.299 × 10⁹⁸(99-digit number)

12990647811758270102…24059900040047696001

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

2.598 × 10⁹⁸(99-digit number)

25981295623516540205…48119800080095391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.598 × 10⁹⁸(99-digit number)

25981295623516540205…48119800080095392001

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

5.196 × 10⁹⁸(99-digit number)

51962591247033080411…96239600160190783999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.196 × 10⁹⁸(99-digit number)

51962591247033080411…96239600160190784001

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

1.039 × 10⁹⁹(100-digit number)

10392518249406616082…92479200320381567999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.039 × 10⁹⁹(100-digit number)

10392518249406616082…92479200320381568001

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