Block #207,761

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 3:12:14 PM · Difficulty 9.9039 · 6,590,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c16e06d58646017c8c10399b820f84815e97a19d4ca81c371d7732f09ba2ba91

View on Chainz ↗

Height

#207,761

Difficulty

9.903921

Transactions

Size

1.58 KB

Version

Bits

09e76756

Nonce

64,323

Timestamp

10/13/2013, 3:12:14 PM

Confirmations

6,590,807

Mined by

⛏️ P2SHAX2TVgXPykg7CCHdx4ieeyhiEw4oFqomRn

Merkle Root

bb6089ac6a4e66a7eb7ed47ef5715a6aa0cc92a107b001820c26cf2d0da4e99f

Transactions (3)

Coinbase5e78236852f5ca…fd10cfe8b13f6c

1 in → 1 out10.2000 XPM109 B

AX2TVgXP…4oFqomRn

1b07c7ea004f2e…15a3f780817d33

3 in → 2 out57.9100 XPM521 B

ARK8Ty8k…FhZFuvMa ARsmaCS8…FVrBGz7H

f785e46cb5c95a…3beaf1089d2d8f

6 in → 1 out63.2266 XPM897 B

AJZMaHsD…y7JtEZqR

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.

6.633 × 10⁹³(94-digit number)

66337503461496796602…08523565546242383619

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

6.633 × 10⁹³(94-digit number)

66337503461496796602…08523565546242383619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.633 × 10⁹³(94-digit number)

66337503461496796602…08523565546242383621

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

1.326 × 10⁹⁴(95-digit number)

13267500692299359320…17047131092484767239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.326 × 10⁹⁴(95-digit number)

13267500692299359320…17047131092484767241

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

2.653 × 10⁹⁴(95-digit number)

26535001384598718640…34094262184969534479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.653 × 10⁹⁴(95-digit number)

26535001384598718640…34094262184969534481

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

5.307 × 10⁹⁴(95-digit number)

53070002769197437281…68188524369939068959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.307 × 10⁹⁴(95-digit number)

53070002769197437281…68188524369939068961

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

1.061 × 10⁹⁵(96-digit number)

10614000553839487456…36377048739878137919

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