Block #546,901

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/16/2014, 3:36:37 AM · Difficulty 10.9567 · 6,279,674 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b258250ec4935a3dbd4574e528a9740a0b66ecc2f0d7140d17ab793b3a558e8f

View on Chainz ↗

Height

#546,901

Difficulty

10.956699

Transactions

Size

809 B

Version

Bits

0af4ea36

Nonce

122,931,398

Timestamp

5/16/2014, 3:36:37 AM

Confirmations

6,279,674

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d9cbe37215af46a0e91209feff16fdc4156127d9de39bee4d6dff7ad6e16fe47

Transactions (3)

Coinbased0029bad64561c…1fdb1215a6bac9

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

e5d9e4e6830f19…d3c9c4e470d6dc

1 in → 2 out5.0922 XPM226 B

ASAk5QVj…qmoG5526 AQsewcDu…xbMc9tDs

ce972997b0adc5…00cf554b4ac9e6

2 in → 2 out1.3731 XPM374 B

AWEm1NVx…BSyUpTdF AePhSBJY…tPVaEP8c

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.

2.914 × 10¹⁰²(103-digit number)

29146138919922056912…66036583325370286079

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

2.914 × 10¹⁰²(103-digit number)

29146138919922056912…66036583325370286079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.914 × 10¹⁰²(103-digit number)

29146138919922056912…66036583325370286081

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

5.829 × 10¹⁰²(103-digit number)

58292277839844113824…32073166650740572159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.829 × 10¹⁰²(103-digit number)

58292277839844113824…32073166650740572161

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

1.165 × 10¹⁰³(104-digit number)

11658455567968822764…64146333301481144319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.165 × 10¹⁰³(104-digit number)

11658455567968822764…64146333301481144321

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

2.331 × 10¹⁰³(104-digit number)

23316911135937645529…28292666602962288639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.331 × 10¹⁰³(104-digit number)

23316911135937645529…28292666602962288641

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

4.663 × 10¹⁰³(104-digit number)

46633822271875291059…56585333205924577279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.663 × 10¹⁰³(104-digit number)

46633822271875291059…56585333205924577281

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

9.326 × 10¹⁰³(104-digit number)

93267644543750582119…13170666411849154559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #546,901

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