Block #81,489

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 7:11:58 PM · Difficulty 9.2697 · 6,713,561 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0e53f70d635043ecf6b4eb5100bd4585b24b2f49a47e91db5967e05915a3abd

View on Chainz ↗

Height

#81,489

Difficulty

9.269741

Transactions

Size

205 B

Version

Bits

09450dc2

Nonce

137,798

Timestamp

7/24/2013, 7:11:58 PM

Confirmations

6,713,561

Mined by

⛏️ P2SHAXGnUfJZw7g3fwFVGKyN2GLpoiBVGAtVkB

Merkle Root

b735473d956b16a45fcec28c087c319dc160b80f1367685b817e167eaf8313b4

Transactions (1)

Coinbaseb735473d956b16…7e167eaf8313b4

1 in → 1 out11.6200 XPM109 B

AXGnUfJZ…BVGAtVkB

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.

2.643 × 10¹⁰⁹(110-digit number)

26432124787862455517…26051749799599928099

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

2.643 × 10¹⁰⁹(110-digit number)

26432124787862455517…26051749799599928099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.643 × 10¹⁰⁹(110-digit number)

26432124787862455517…26051749799599928101

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

5.286 × 10¹⁰⁹(110-digit number)

52864249575724911034…52103499599199856199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.286 × 10¹⁰⁹(110-digit number)

52864249575724911034…52103499599199856201

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

1.057 × 10¹¹⁰(111-digit number)

10572849915144982206…04206999198399712399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.057 × 10¹¹⁰(111-digit number)

10572849915144982206…04206999198399712401

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

2.114 × 10¹¹⁰(111-digit number)

21145699830289964413…08413998396799424799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.114 × 10¹¹⁰(111-digit number)

21145699830289964413…08413998396799424801

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

4.229 × 10¹¹⁰(111-digit number)

42291399660579928827…16827996793598849599

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