Block #56,463

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/17/2013, 8:11:37 AM · Difficulty 8.9488 · 6,737,327 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5bc05d62e829330a84289e149dcf31a48c004ae7d758572d2ad38075d59274ae

View on Chainz ↗

Height

#56,463

Difficulty

8.948801

Transactions

Size

5.00 KB

Version

Bits

08f2e4a5

Nonce

260

Timestamp

7/17/2013, 8:11:37 AM

Confirmations

6,737,327

Merkle Root

ad3059d45f26940913e40694e286f59197799dbe8cf0833cab471f02803244cf

Transactions (5)

Coinbase569717633c0b64…c1f18f555a0bba

1 in → 1 out12.5500 XPM110 B

AL7U24rM…GGYNCSDc

ceefd463948c23…02f38910213368

5 in → 1 out89.3100 XPM615 B

AXrnbEwV…3q35rj57

c2ccc21f8dcb93…406c3ad1c14440

34 in → 1 out500.0000 XPM3.89 KB

AZp4avYs…pV5KGy9w

576f7f5571dfae…2de40f7e230902

1 in → 1 out13.2300 XPM157 B

AKAKDL9k…K6NVTqpR

3c3ae7b8f3ce6b…19fb88aaa8d502

1 in → 1 out12.8700 XPM159 B

AKAKDL9k…K6NVTqpR

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.

7.992 × 10¹⁰⁰(101-digit number)

79921536988567616115…93586934468329079999

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

7.992 × 10¹⁰⁰(101-digit number)

79921536988567616115…93586934468329079999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.992 × 10¹⁰⁰(101-digit number)

79921536988567616115…93586934468329080001

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

1.598 × 10¹⁰¹(102-digit number)

15984307397713523223…87173868936658159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.598 × 10¹⁰¹(102-digit number)

15984307397713523223…87173868936658160001

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

3.196 × 10¹⁰¹(102-digit number)

31968614795427046446…74347737873316319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.196 × 10¹⁰¹(102-digit number)

31968614795427046446…74347737873316320001

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

6.393 × 10¹⁰¹(102-digit number)

63937229590854092892…48695475746632639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.393 × 10¹⁰¹(102-digit number)

63937229590854092892…48695475746632640001

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

1.278 × 10¹⁰²(103-digit number)

12787445918170818578…97390951493265279999

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