Block #116,300

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/14/2013, 8:05:41 AM · Difficulty 9.7474 · 6,681,518 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aea758f0a9e3c33567d7ff390fe126c1ae6d77a55600fc71ad2783c27b39d12d

View on Chainz ↗

Height

#116,300

Difficulty

9.747425

Transactions

Size

723 B

Version

Bits

09bf573d

Nonce

18,321

Timestamp

8/14/2013, 8:05:41 AM

Confirmations

6,681,518

Mined by

⛏️ P2SHAGELmJR6aPRjt3Z8ALYc9YsGpGUuQ4Rhjr

Merkle Root

50e62264f492507f00cd5275b661ae4bc404848d6f2b017ef836fb8c67ea92f3

Transactions (2)

Coinbaseb32981d1ad286a…a19b32962f5f20

1 in → 1 out10.5200 XPM109 B

AGELmJR6…UuQ4Rhjr

94ddedd73b0af6…4ccac12cd5d742

3 in → 2 out200.0104 XPM523 B

AYPBsr3p…ChMVeAkL APNAcJ2U…oFHVmce7

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.

8.499 × 10⁹⁵(96-digit number)

84990227523805471699…60286610138722979999

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

8.499 × 10⁹⁵(96-digit number)

84990227523805471699…60286610138722979999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.499 × 10⁹⁵(96-digit number)

84990227523805471699…60286610138722980001

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

1.699 × 10⁹⁶(97-digit number)

16998045504761094339…20573220277445959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.699 × 10⁹⁶(97-digit number)

16998045504761094339…20573220277445960001

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

3.399 × 10⁹⁶(97-digit number)

33996091009522188679…41146440554891919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.399 × 10⁹⁶(97-digit number)

33996091009522188679…41146440554891920001

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

6.799 × 10⁹⁶(97-digit number)

67992182019044377359…82292881109783839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.799 × 10⁹⁶(97-digit number)

67992182019044377359…82292881109783840001

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

1.359 × 10⁹⁷(98-digit number)

13598436403808875471…64585762219567679999

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