Block #135,006

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 9:20:26 AM · Difficulty 9.8077 · 6,673,857 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

008eb1c3933cc2f047825637f61964a8ab42437ce6f18c594edbe32e99126ab3

View on Chainz ↗

Height

#135,006

Difficulty

9.807672

Transactions

Size

1.22 KB

Version

Bits

09cec39b

Nonce

126,451

Timestamp

8/26/2013, 9:20:26 AM

Confirmations

6,673,857

Mined by

⛏️ P2SHAGYNx3UhtU7R67g7CdmKN8zyR1ef87iHu1

Merkle Root

5fe5cef97b19b169dc61e3e68beb3fe9d3672fe50337fa5339621d88c1f18b85

Transactions (5)

Coinbaseaea49d0d45c724…25862654afb1ea

1 in → 1 out10.4200 XPM109 B

AGYNx3Uh…ef87iHu1

f07e92c02fc5d7…63cc4060dab027

1 in → 2 out8.4045 XPM226 B

ANN8gjLH…8ToruqzW AL5by2YM…iAbDrS57

6593d2f9471480…7f9fd3853e8163

1 in → 2 out3.1020 XPM225 B

AX6VfiSu…eRSBv1z1 ANUPa5nC…gS5uF4Pm

62db9a79b1e081…069ad1b2f84738

1 in → 2 out4.6047 XPM226 B

AUfBNY3y…Mm2UYiNj ASCFbCGf…Q4TL3zTc

2c6b3f17af15f0…734a05a0488c3a

2 in → 2 out10.2577 XPM375 B

ALp4QBZx…yAnNHja9 ANZrFK7s…egwB9Mmt

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.

2.878 × 10¹⁰²(103-digit number)

28787614771968507884…90991882425633616319

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

2.878 × 10¹⁰²(103-digit number)

28787614771968507884…90991882425633616319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.878 × 10¹⁰²(103-digit number)

28787614771968507884…90991882425633616321

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

5.757 × 10¹⁰²(103-digit number)

57575229543937015769…81983764851267232639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.757 × 10¹⁰²(103-digit number)

57575229543937015769…81983764851267232641

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

1.151 × 10¹⁰³(104-digit number)

11515045908787403153…63967529702534465279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.151 × 10¹⁰³(104-digit number)

11515045908787403153…63967529702534465281

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

2.303 × 10¹⁰³(104-digit number)

23030091817574806307…27935059405068930559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.303 × 10¹⁰³(104-digit number)

23030091817574806307…27935059405068930561

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

4.606 × 10¹⁰³(104-digit number)

46060183635149612615…55870118810137861119

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 #135,006

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