Block #216,029

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 12:18:09 PM · Difficulty 9.9254 · 6,593,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a46b6b99a656df2edc5736daa2b61b61a29ab626e26f56c55fa410293a116bdf

View on Chainz ↗

Height

#216,029

Difficulty

9.925373

Transactions

Size

1.08 KB

Version

Bits

09ece539

Nonce

83,765

Timestamp

10/18/2013, 12:18:09 PM

Confirmations

6,593,700

Mined by

⛏️ P2SHAVDWXkeYRc1J7RNt5eSeqHs4JbEigwWXVy

Merkle Root

0b495e4962aa803cdae689581fab429e1a439771456a8d176c970eca41f393ec

Transactions (5)

Coinbase11803166164f3e…a5147108f679bd

1 in → 1 out10.1800 XPM109 B

AVDWXkeY…EigwWXVy

02a58d27c30793…89c2e1112cb60c

1 in → 2 out10.1400 XPM227 B

ARpYgZBo…PeLmQCxy Abw8D7Bc…EioKVM91

c061cbdc0dfcc1…f01bcab5ab2897

1 in → 2 out10.1400 XPM225 B

AX1BA5wJ…YuiP7NfY ANShBaCx…NttHiwPk

51a64ed81a4e19…eac653b166f2a2

1 in → 2 out10.1400 XPM226 B

ANq6Hy7m…86xjrm8N Acte3A2t…Am77BrgQ

a177a96f4c69fb…402e282e0d4661

1 in → 2 out8.1260 XPM225 B

AWRFK6bo…fyaT5SNs AU9P8eaV…ZYFUiAC5

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.

4.649 × 10⁹²(93-digit number)

46493969158057480804…19339664825035239679

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

4.649 × 10⁹²(93-digit number)

46493969158057480804…19339664825035239679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.649 × 10⁹²(93-digit number)

46493969158057480804…19339664825035239681

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

9.298 × 10⁹²(93-digit number)

92987938316114961609…38679329650070479359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.298 × 10⁹²(93-digit number)

92987938316114961609…38679329650070479361

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

1.859 × 10⁹³(94-digit number)

18597587663222992321…77358659300140958719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.859 × 10⁹³(94-digit number)

18597587663222992321…77358659300140958721

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

3.719 × 10⁹³(94-digit number)

37195175326445984643…54717318600281917439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.719 × 10⁹³(94-digit number)

37195175326445984643…54717318600281917441

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

7.439 × 10⁹³(94-digit number)

74390350652891969287…09434637200563834879

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

Block #216,029

Cookie Preferences