Block #299,638

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 2:28:11 AM · Difficulty 9.9921 · 6,498,523 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f2a23f6cb3fb621babc560cfda077c53582da54c51650f9ad5f31eace21d0af9

View on Chainz ↗

Height

#299,638

Difficulty

9.992147

Transactions

Size

2.45 KB

Version

Bits

09fdfd53

Nonce

563,879

Timestamp

12/8/2013, 2:28:11 AM

Confirmations

6,498,523

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

91b22cca921cf1a233f06c7da01436f08bc4f0c904f75c543aaf97a6ecd2240f

Transactions (4)

Coinbase6609accf63f7e1…24c9fdd3d66039

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

0d1ead69fdcf05…58a1e4dcac8e4c

1 in → 2 out4182.7052 XPM226 B

AaWZJEh6…xg8gB5gZ AXXzDX34…wM8GZcM5

a41a4fd2a1604e…a7ef607fcaebb3

1 in → 2 out608.9498 XPM225 B

AGp1TkDG…BbekPRJG ALrxtRZB…pgpnxSCZ

ecb48a080fb2b7…39a3cb7afc5b52

12 in → 2 out3.1174 XPM1.81 KB

AWZoaFiX…YzJJ81GU AexZoj71…Z7FmawVi

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.

2.900 × 10⁹⁵(96-digit number)

29002937299309233803…54135304830533021999

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

2.900 × 10⁹⁵(96-digit number)

29002937299309233803…54135304830533021999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.900 × 10⁹⁵(96-digit number)

29002937299309233803…54135304830533022001

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

5.800 × 10⁹⁵(96-digit number)

58005874598618467606…08270609661066043999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.800 × 10⁹⁵(96-digit number)

58005874598618467606…08270609661066044001

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

1.160 × 10⁹⁶(97-digit number)

11601174919723693521…16541219322132087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.160 × 10⁹⁶(97-digit number)

11601174919723693521…16541219322132088001

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

2.320 × 10⁹⁶(97-digit number)

23202349839447387042…33082438644264175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.320 × 10⁹⁶(97-digit number)

23202349839447387042…33082438644264176001

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

4.640 × 10⁹⁶(97-digit number)

46404699678894774085…66164877288528351999

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