Block #576,945

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/4/2014, 10:54:33 PM · Difficulty 10.9689 · 6,230,635 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

98db85e676cb52fb7d7454d314f28e5b11ee0d3ef5173638d4260e6bcae9568b

View on Chainz ↗

Height

#576,945

Difficulty

10.968853

Transactions

Size

1.08 KB

Version

Bits

0af806b9

Nonce

449,502,193

Timestamp

6/4/2014, 10:54:33 PM

Confirmations

6,230,635

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b3791be1318cc0df3cce002dcd69c16f4a8ce998754084b74fb3db0a6ff97b87

Transactions (5)

Coinbase84b6e68e08c830…436b27cf1edbf9

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

0b81efc68d1b44…687493f9d8e187

1 in → 2 out7.6445 XPM226 B

APb2PYuY…rUArnCvE AGdWVjRk…LFVsqCnK

3dd3760c379085…698570bb9228f9

1 in → 2 out7.2778 XPM225 B

AFvXyDeW…4QQrCTPJ ANxFUUpp…JdLqwmVd

e662d6f6e78d2b…307f70f46e92af

1 in → 2 out2.8501 XPM225 B

AJTsLJ89…rErdMt2e ALD33gRD…k7V94uf3

152bbcad2bde4b…964e3fa67bce06

1 in → 2 out3.6131 XPM226 B

ALJPqMZ2…beUMMCwy AQYfM6tR…wtD7VsKo

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.

1.230 × 10¹⁰⁰(101-digit number)

12300676056890195558…46793344944469688319

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

1.230 × 10¹⁰⁰(101-digit number)

12300676056890195558…46793344944469688319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.230 × 10¹⁰⁰(101-digit number)

12300676056890195558…46793344944469688321

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

2.460 × 10¹⁰⁰(101-digit number)

24601352113780391117…93586689888939376639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.460 × 10¹⁰⁰(101-digit number)

24601352113780391117…93586689888939376641

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

4.920 × 10¹⁰⁰(101-digit number)

49202704227560782234…87173379777878753279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.920 × 10¹⁰⁰(101-digit number)

49202704227560782234…87173379777878753281

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

9.840 × 10¹⁰⁰(101-digit number)

98405408455121564469…74346759555757506559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.840 × 10¹⁰⁰(101-digit number)

98405408455121564469…74346759555757506561

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

1.968 × 10¹⁰¹(102-digit number)

19681081691024312893…48693519111515013119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.968 × 10¹⁰¹(102-digit number)

19681081691024312893…48693519111515013121

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #576,945

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