Block #575,392

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/3/2014, 10:32:08 PM · Difficulty 10.9682 · 6,241,557 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6f436f6085dcaf19011bafa78c61a12d6087a99c27001dfea0b2429661ec8fb

View on Chainz ↗

Height

#575,392

Difficulty

10.968237

Transactions

Size

1.59 KB

Version

Bits

0af7de5d

Nonce

349,156,097

Timestamp

6/3/2014, 10:32:08 PM

Confirmations

6,241,557

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ca264ff891b994b0231f8e961ac4a3352ef86240cd9bbb4d373ee750d9471643

Transactions (4)

Coinbasec4045094ed5eea…305c2e168903c4

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

9466a0bf980cae…8934b94a58793a

5 in → 2 out400.1356 XPM818 B

AHAWsE5q…88AHeq2Z AMVewuan…8Ng916Zh

d3c1416afd9aa7…ecb308a32c05d0

2 in → 2 out14.5108 XPM375 B

AWAbb2pL…4Wmht5QK AYu9BRVy…iKXRmaSR

7d358165fb9cdd…cb9712934da412

1 in → 2 out1.3609 XPM227 B

Aavj3FfW…t1VYCmvw AekdwfxU…kbhJFGTn

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.

2.511 × 10⁹⁷(98-digit number)

25112399515150488739…33332599127773593279

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

2.511 × 10⁹⁷(98-digit number)

25112399515150488739…33332599127773593279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.511 × 10⁹⁷(98-digit number)

25112399515150488739…33332599127773593281

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

5.022 × 10⁹⁷(98-digit number)

50224799030300977479…66665198255547186559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.022 × 10⁹⁷(98-digit number)

50224799030300977479…66665198255547186561

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

1.004 × 10⁹⁸(99-digit number)

10044959806060195495…33330396511094373119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.004 × 10⁹⁸(99-digit number)

10044959806060195495…33330396511094373121

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

2.008 × 10⁹⁸(99-digit number)

20089919612120390991…66660793022188746239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.008 × 10⁹⁸(99-digit number)

20089919612120390991…66660793022188746241

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

4.017 × 10⁹⁸(99-digit number)

40179839224240781983…33321586044377492479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.017 × 10⁹⁸(99-digit number)

40179839224240781983…33321586044377492481

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

8.035 × 10⁹⁸(99-digit number)

80359678448481563966…66643172088754984959

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 #575,392

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