Block #215,806

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 8:28:22 AM · Difficulty 9.9254 · 6,575,463 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4332270dfa79406b3541b31f8b23cebc6fe2bd1718121ab2e3f3ed550aa0c4ee

View on Chainz ↗

Height

#215,806

Difficulty

9.925438

Transactions

Size

1.80 KB

Version

Bits

09ece97a

Nonce

48,943

Timestamp

10/18/2013, 8:28:22 AM

Confirmations

6,575,463

Merkle Root

a4e8fdc466adad5f09d8c7001e237f1f0bd23ce76a224190eec7ef3ae71cea2e

Transactions (5)

Coinbase288391fd530c5f…faa38c0cfe30e7

1 in → 1 out10.1800 XPM110 B

AbuU1HhS…JPwsJEbB

ed06c041cde225…fcaa5d1fa536bc

1 in → 2 out10.1400 XPM226 B

ARdEFcSb…mQoSgqJL AStDMMwD…P5zgHmx7

f3a129f5bcfa89…8646310d9cb3e1

1 in → 2 out10.1400 XPM227 B

AaVFHFSq…bCnX1Bpw AZjV1ezU…uyFK4Vxe

579539492256ae…2e484e7e90a2cc

2 in → 2 out2.0589 XPM373 B

AaCf5S6v…axNLRNYQ AdWp2YRv…FDtt217a

ebf03cfcbae864…e173a5a760c205

5 in → 2 out5.0802 XPM819 B

AKTcMgGK…nyDf5doz ALBELHXn…v353RSWb

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.

1.409 × 10⁹⁴(95-digit number)

14093437860218201018…52471945363770891359

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

1.409 × 10⁹⁴(95-digit number)

14093437860218201018…52471945363770891359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.409 × 10⁹⁴(95-digit number)

14093437860218201018…52471945363770891361

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

2.818 × 10⁹⁴(95-digit number)

28186875720436402037…04943890727541782719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.818 × 10⁹⁴(95-digit number)

28186875720436402037…04943890727541782721

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

5.637 × 10⁹⁴(95-digit number)

56373751440872804075…09887781455083565439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.637 × 10⁹⁴(95-digit number)

56373751440872804075…09887781455083565441

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

1.127 × 10⁹⁵(96-digit number)

11274750288174560815…19775562910167130879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.127 × 10⁹⁵(96-digit number)

11274750288174560815…19775562910167130881

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

2.254 × 10⁹⁵(96-digit number)

22549500576349121630…39551125820334261759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.254 × 10⁹⁵(96-digit number)

22549500576349121630…39551125820334261761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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