Block #213,929

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 3:51:43 AM · Difficulty 9.9228 · 6,591,285 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e242b076ba0065e94bdc21b237b9f465597448d7306af663ca1b2034177a675

View on Chainz ↗

Height

#213,929

Difficulty

9.922789

Transactions

Size

1.47 KB

Version

Bits

09ec3be2

Nonce

27,769

Timestamp

10/17/2013, 3:51:43 AM

Confirmations

6,591,285

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

c29448c3e8b19794b64fe178645bbada8e2a4b9d440c063aabf3268702171dfb

Transactions (3)

Coinbase2af491751e4a62…fa55be72cc4022

1 in → 1 out10.1700 XPM110 B

AbuU1HhS…JPwsJEbB

1313b71aa1a9d4…5e6e0c21c874a6

5 in → 2 out569.8044 XPM814 B

AY2m3BFm…Pm2nQTFt AMAYMEKe…9xu4iX9j

a0b8ae4c14f672…735371ea435580

3 in → 4 out30.5100 XPM488 B

AbuU1HhS…JPwsJEbB AHLyZUb7…cHnQjZJ9 AQXUSoBL…CzbjKp8b AUfa5LFJ…C4BhhWGa

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.

5.563 × 10⁹³(94-digit number)

55630713600532344147…77071540157390630399

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

5.563 × 10⁹³(94-digit number)

55630713600532344147…77071540157390630399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.563 × 10⁹³(94-digit number)

55630713600532344147…77071540157390630401

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

1.112 × 10⁹⁴(95-digit number)

11126142720106468829…54143080314781260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.112 × 10⁹⁴(95-digit number)

11126142720106468829…54143080314781260801

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

2.225 × 10⁹⁴(95-digit number)

22252285440212937658…08286160629562521599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.225 × 10⁹⁴(95-digit number)

22252285440212937658…08286160629562521601

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

4.450 × 10⁹⁴(95-digit number)

44504570880425875317…16572321259125043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.450 × 10⁹⁴(95-digit number)

44504570880425875317…16572321259125043201

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

8.900 × 10⁹⁴(95-digit number)

89009141760851750635…33144642518250086399

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