Block #80,633

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/24/2013, 6:45:08 AM · Difficulty 9.2539 · 6,711,034 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59f41762ef40bc05c2e6f6941a053e5790c9401bd9428dfcbffd490c850bda0f

View on Chainz ↗

Height

#80,633

Difficulty

9.253889

Transactions

Size

1.13 KB

Version

Bits

0940fee0

Nonce

20,813

Timestamp

7/24/2013, 6:45:08 AM

Confirmations

6,711,034

Merkle Root

fc4540f87366d58dfd6152ba84192f4211d21224bb7c9a574ae220a7ba4509eb

Transactions (4)

Coinbasedc0a6fbff23285…f58e3e9265298a

1 in → 1 out11.6900 XPM109 B

ALfougru…epVg8jEc

ef1ff04b12d747…c0af01d437ffe2

2 in → 1 out24.6800 XPM274 B

AQpb4giu…JkhEj932

a7bdc6ece71931…4e9acef490f70c

3 in → 2 out200.0208 XPM521 B

AdGYnqoY…pjMuwV34 AZ9shFUa…2rZ6YMTu

af965d36622715…004ba7ec1b0540

1 in → 1 out11.9600 XPM158 B

AUyL3rcf…PuULqq4T

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.

7.809 × 10¹⁰³(104-digit number)

78090939019458285632…73176878036207779979

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

7.809 × 10¹⁰³(104-digit number)

78090939019458285632…73176878036207779979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.809 × 10¹⁰³(104-digit number)

78090939019458285632…73176878036207779981

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

1.561 × 10¹⁰⁴(105-digit number)

15618187803891657126…46353756072415559959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.561 × 10¹⁰⁴(105-digit number)

15618187803891657126…46353756072415559961

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

3.123 × 10¹⁰⁴(105-digit number)

31236375607783314252…92707512144831119919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.123 × 10¹⁰⁴(105-digit number)

31236375607783314252…92707512144831119921

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

6.247 × 10¹⁰⁴(105-digit number)

62472751215566628505…85415024289662239839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.247 × 10¹⁰⁴(105-digit number)

62472751215566628505…85415024289662239841

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

1.249 × 10¹⁰⁵(106-digit number)

12494550243113325701…70830048579324479679

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