Block #80,801

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 9:13:35 AM · Difficulty 9.2565 · 6,713,386 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eef935c60de94e5a3844202b4c9114d4bddba04a0c085089c4024249855f2618

View on Chainz ↗

Height

#80,801

Difficulty

9.256522

Transactions

Size

1.14 KB

Version

Bits

0941ab68

Nonce

Timestamp

7/24/2013, 9:13:35 AM

Confirmations

6,713,386

Merkle Root

ec345b1948be6750c6cfab2fccb567f1136981cd3cc39edbc763790e94f29e53

Transactions (2)

Coinbasee5969642eb9662…e2bb5933030021

1 in → 1 out11.6600 XPM110 B

AYoowFBo…GoBQmagv

8bd8eada4abc32…a646464a9ae6c2

6 in → 2 out163.9173 XPM964 B

AKVZmjFY…iuD64V6a AUo9iFd3…y6BCMx4n

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.

6.502 × 10¹⁰⁴(105-digit number)

65023501894706867129…30082208495452956239

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

6.502 × 10¹⁰⁴(105-digit number)

65023501894706867129…30082208495452956239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.502 × 10¹⁰⁴(105-digit number)

65023501894706867129…30082208495452956241

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

1.300 × 10¹⁰⁵(106-digit number)

13004700378941373425…60164416990905912479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.300 × 10¹⁰⁵(106-digit number)

13004700378941373425…60164416990905912481

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

2.600 × 10¹⁰⁵(106-digit number)

26009400757882746851…20328833981811824959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.600 × 10¹⁰⁵(106-digit number)

26009400757882746851…20328833981811824961

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

5.201 × 10¹⁰⁵(106-digit number)

52018801515765493703…40657667963623649919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.201 × 10¹⁰⁵(106-digit number)

52018801515765493703…40657667963623649921

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

1.040 × 10¹⁰⁶(107-digit number)

10403760303153098740…81315335927247299839

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