Block #200,863

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 6:50:29 AM · Difficulty 9.8905 · 6,591,118 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d438f956e2c3ff8fdb3c693259494a43cc7b551b7c79bdb1a61b946d6470a3e

View on Chainz ↗

Height

#200,863

Difficulty

9.890493

Transactions

Size

1.08 KB

Version

Bits

09e3f760

Nonce

29,137

Timestamp

10/9/2013, 6:50:29 AM

Confirmations

6,591,118

Merkle Root

a07a373ccbde61b7cedb424e410740fd7fd96bf89a4efb0452693c6c4cd5d514

Transactions (4)

Coinbasebf558cb3014dda…ec952c24b090b1

1 in → 1 out10.2400 XPM110 B

AFvfCa1W…3pZgbFWa

7e3e766ad49cc1…d60c6556236d6d

1 in → 2 out10.2100 XPM227 B

AaFS7HMR…cYdjV9Di AeNo3RVm…WruQcTwE

6f041cfb967050…6062df2efe8d76

2 in → 1 out10.5300 XPM305 B

AVA5pcCT…FNQyZZmf

f208661827c29c…5c7dc20b013f7b

2 in → 2 out11.1833 XPM374 B

ASuoUi24…FwBoFbxd ALUszu4L…BiK7kM6B

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.

1.013 × 10⁹³(94-digit number)

10138147048514075670…57443385594307839999

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

1.013 × 10⁹³(94-digit number)

10138147048514075670…57443385594307839999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.013 × 10⁹³(94-digit number)

10138147048514075670…57443385594307840001

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

2.027 × 10⁹³(94-digit number)

20276294097028151340…14886771188615679999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.027 × 10⁹³(94-digit number)

20276294097028151340…14886771188615680001

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

4.055 × 10⁹³(94-digit number)

40552588194056302680…29773542377231359999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.055 × 10⁹³(94-digit number)

40552588194056302680…29773542377231360001

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

8.110 × 10⁹³(94-digit number)

81105176388112605360…59547084754462719999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.110 × 10⁹³(94-digit number)

81105176388112605360…59547084754462720001

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

1.622 × 10⁹⁴(95-digit number)

16221035277622521072…19094169508925439999

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