Block #550,673

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/18/2014, 8:05:55 AM · Difficulty 10.9618 · 6,258,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

293ebd5352229b3cedfefaceb8ca38cdc9f713bed05085cfeec7ac86377aefbe

View on Chainz ↗

Height

#550,673

Difficulty

10.961836

Transactions

Size

436 B

Version

Bits

0af63ae4

Nonce

115,600,888

Timestamp

5/18/2014, 8:05:55 AM

Confirmations

6,258,058

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b02131feb662c6dbfb9f748a1d78c1a6ba8136b5ce57b991b7c593f54e7e37a3

Transactions (2)

Coinbasebb29e874a6fac5…d1ddba8dd739ca

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

c7a18c3799f48b…c5a56284d90f08

1 in → 2 out5.1711 XPM227 B

AeKNrjNj…1NEq95Ta Ad5rowoZ…YCVsFMcc

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.

1.450 × 10¹⁰¹(102-digit number)

14507651461540854976…14242528374614507519

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

1.450 × 10¹⁰¹(102-digit number)

14507651461540854976…14242528374614507519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.450 × 10¹⁰¹(102-digit number)

14507651461540854976…14242528374614507521

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

2.901 × 10¹⁰¹(102-digit number)

29015302923081709952…28485056749229015039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.901 × 10¹⁰¹(102-digit number)

29015302923081709952…28485056749229015041

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

5.803 × 10¹⁰¹(102-digit number)

58030605846163419904…56970113498458030079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.803 × 10¹⁰¹(102-digit number)

58030605846163419904…56970113498458030081

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

1.160 × 10¹⁰²(103-digit number)

11606121169232683980…13940226996916060159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.160 × 10¹⁰²(103-digit number)

11606121169232683980…13940226996916060161

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

2.321 × 10¹⁰²(103-digit number)

23212242338465367961…27880453993832120319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.321 × 10¹⁰²(103-digit number)

23212242338465367961…27880453993832120321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.642 × 10¹⁰²(103-digit number)

46424484676930735923…55760907987664240639

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

4.642 × 10¹⁰²(103-digit number)

46424484676930735923…55760907987664240641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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

Block #550,673

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