Block #116,008

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/14/2013, 3:57:00 AM · Difficulty 9.7452 · 6,689,739 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d3b0a81af7101901c4335b6372280192106ded3ce3567664c1d922756198b242

View on Chainz ↗

Height

#116,008

Difficulty

9.745248

Transactions

Size

1.05 KB

Version

Bits

09bec894

Nonce

47,630

Timestamp

8/14/2013, 3:57:00 AM

Confirmations

6,689,739

Mined by

⛏️ P2SHAJLESN6LKrAA4RndPVDerxq7QyAMrt76tG

Merkle Root

46c70c6c93733808f0fd8d47839a6f21982def9cfc310fdacc657332a95b1d18

Transactions (5)

Coinbase929d8bb395d2fb…428f0f73d3e7cc

1 in → 1 out10.5500 XPM109 B

AJLESN6L…AMrt76tG

1bca43861e0129…45516ccea3f446

1 in → 2 out10.5500 XPM227 B

AYPyNwRS…ZEdPVp5X AaamjEDB…UqchbkWj

fd00f6b4f569e1…67e862fa790485

1 in → 2 out10.5500 XPM226 B

ARRdbjnk…Bvquyg3e APwXmRMD…5F7RDjwG

385c207de2194e…bffda9937f07c8

1 in → 2 out5.5257 XPM227 B

AdqZEjD1…ZfnUQEpe AGcQsbk1…x5Qx3xFw

7f31f5d17fce39…6a3be957558896

1 in → 1 out1.9900 XPM192 B

AGsjwwbj…Fq54UcrM

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.

2.101 × 10⁹⁸(99-digit number)

21011051952141517548…58515151427628115759

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

2.101 × 10⁹⁸(99-digit number)

21011051952141517548…58515151427628115759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.101 × 10⁹⁸(99-digit number)

21011051952141517548…58515151427628115761

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

4.202 × 10⁹⁸(99-digit number)

42022103904283035097…17030302855256231519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.202 × 10⁹⁸(99-digit number)

42022103904283035097…17030302855256231521

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

8.404 × 10⁹⁸(99-digit number)

84044207808566070194…34060605710512463039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.404 × 10⁹⁸(99-digit number)

84044207808566070194…34060605710512463041

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

1.680 × 10⁹⁹(100-digit number)

16808841561713214038…68121211421024926079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.680 × 10⁹⁹(100-digit number)

16808841561713214038…68121211421024926081

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

3.361 × 10⁹⁹(100-digit number)

33617683123426428077…36242422842049852159

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