Block #77,261

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 8:43:04 AM · Difficulty 9.1572 · 6,712,675 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26f7c14fc2da584719e5fa18b3a9d778d7f6820a5c583a9a3250935bf12cb23c

View on Chainz ↗

Height

#77,261

Difficulty

9.157200

Transactions

Size

204 B

Version

Bits

09283e44

Nonce

199

Timestamp

7/22/2013, 8:43:04 AM

Confirmations

6,712,675

Merkle Root

a207eda501aaedbf10caa106670798b6927f37ed4f0f060f95b7d8a6d960140f

Transactions (1)

Coinbasea207eda501aaed…b7d8a6d960140f

1 in → 1 out11.9100 XPM110 B

AK1JUKWL…oPR4rN5o

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.

1.101 × 10¹⁰⁵(106-digit number)

11015846531868938265…78275388348736963359

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

1.101 × 10¹⁰⁵(106-digit number)

11015846531868938265…78275388348736963359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.101 × 10¹⁰⁵(106-digit number)

11015846531868938265…78275388348736963361

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

2.203 × 10¹⁰⁵(106-digit number)

22031693063737876530…56550776697473926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.203 × 10¹⁰⁵(106-digit number)

22031693063737876530…56550776697473926721

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

4.406 × 10¹⁰⁵(106-digit number)

44063386127475753061…13101553394947853439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.406 × 10¹⁰⁵(106-digit number)

44063386127475753061…13101553394947853441

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

8.812 × 10¹⁰⁵(106-digit number)

88126772254951506123…26203106789895706879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.812 × 10¹⁰⁵(106-digit number)

88126772254951506123…26203106789895706881

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

1.762 × 10¹⁰⁶(107-digit number)

17625354450990301224…52406213579791413759

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