Block #216,297

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 4:01:41 PM · Difficulty 9.9260 · 6,575,457 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02f89a501416f3f6e938aedadc60b0f82493fc26bcdab26fae853bea8a01bdad

View on Chainz ↗

Height

#216,297

Difficulty

9.925990

Transactions

Size

1.44 KB

Version

Bits

09ed0daa

Nonce

125,149

Timestamp

10/18/2013, 4:01:41 PM

Confirmations

6,575,457

Merkle Root

3fc0da76a7fb12429c02e16d6a89a78a135779b434735566add6381b2080f1b8

Transactions (4)

Coinbase067863b787a532…330560d7c1d722

1 in → 1 out10.1600 XPM109 B

AHkHp3VQ…1tWPfSyN

2a8da02be7e320…4d7be5eecf2709

3 in → 2 out10.2826 XPM521 B

AKqHhpcP…QrDbeRa9 AJhgf59P…W42GoeAR

4c1ebda6d30825…e69cbea86869ee

2 in → 2 out3.9945 XPM374 B

ATRRKo67…MoETsBbP AepBuXhC…nuU7jDvn

aa97fcb12f19ca…db0858f7852a11

2 in → 2 out2.1098 XPM374 B

Act2yiz3…rKQfPDe8 AFyuHBLS…vVkR2Gq5

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.

7.137 × 10⁹⁸(99-digit number)

71377820464604889708…59247581801587343359

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

7.137 × 10⁹⁸(99-digit number)

71377820464604889708…59247581801587343359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.137 × 10⁹⁸(99-digit number)

71377820464604889708…59247581801587343361

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

1.427 × 10⁹⁹(100-digit number)

14275564092920977941…18495163603174686719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.427 × 10⁹⁹(100-digit number)

14275564092920977941…18495163603174686721

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

2.855 × 10⁹⁹(100-digit number)

28551128185841955883…36990327206349373439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.855 × 10⁹⁹(100-digit number)

28551128185841955883…36990327206349373441

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

5.710 × 10⁹⁹(100-digit number)

57102256371683911766…73980654412698746879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.710 × 10⁹⁹(100-digit number)

57102256371683911766…73980654412698746881

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

1.142 × 10¹⁰⁰(101-digit number)

11420451274336782353…47961308825397493759

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