Block #81,097

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 1:13:30 PM · Difficulty 9.2647 · 6,708,662 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a8819c77b71de4e5b199f86b9cf3d0e7e2565f6ec4518ab28bf9f4824af017d

View on Chainz ↗

Height

#81,097

Difficulty

9.264729

Transactions

Size

1.14 KB

Version

Bits

0943c54e

Nonce

Timestamp

7/24/2013, 1:13:30 PM

Confirmations

6,708,662

Merkle Root

5a2a713aedc924164454a4f1b96f3406d53af4f4963302ffcc7058ea87c82eac

Transactions (2)

Coinbasede34533b064537…b539940a489fe9

1 in → 1 out11.6400 XPM110 B

AGnu2zG4…rgLSMxn8

9d4e1281615058…35010bed35bf0a

6 in → 2 out449.1092 XPM964 B

AW3oqdog…1qjNKMmh AG8LEEmQ…YosJ1kAe

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.

3.744 × 10⁹⁶(97-digit number)

37444723635754467127…92789811185733925679

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

3.744 × 10⁹⁶(97-digit number)

37444723635754467127…92789811185733925679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.744 × 10⁹⁶(97-digit number)

37444723635754467127…92789811185733925681

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

7.488 × 10⁹⁶(97-digit number)

74889447271508934255…85579622371467851359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.488 × 10⁹⁶(97-digit number)

74889447271508934255…85579622371467851361

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

1.497 × 10⁹⁷(98-digit number)

14977889454301786851…71159244742935702719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.497 × 10⁹⁷(98-digit number)

14977889454301786851…71159244742935702721

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

2.995 × 10⁹⁷(98-digit number)

29955778908603573702…42318489485871405439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.995 × 10⁹⁷(98-digit number)

29955778908603573702…42318489485871405441

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

5.991 × 10⁹⁷(98-digit number)

59911557817207147404…84636978971742810879

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