Block #530,813

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/8/2014, 2:54:15 AM · Difficulty 10.8929 · 6,277,661 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b03042c8163d3ec868631bc542ac110672aa0adf0ddd0759ebb1906505da3f46

View on Chainz ↗

Height

#530,813

Difficulty

10.892914

Transactions

Size

1.44 KB

Version

Bits

0ae49606

Nonce

1,039,856

Timestamp

5/8/2014, 2:54:15 AM

Confirmations

6,277,661

Mined by

⛏️ }aSj!AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

98bf20cf8d0609bb71782c549dc60d135e8a6309af6a2501befdd4f2b3e02b1b

Transactions (4)

Coinbasef11fc5d06fb948…064e174934fb59

1 in → 19 out8.4100 XPM709 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j ATKK7iFz…wZm46KN1

2950ffb266845f…13ad49219bf2af

1 in → 2 out7.1204 XPM225 B

ATTj3Quj…RogtXXPS AGVu5ruv…Z7JNwydH

03c1521625a575…e28dc2a5acf322

1 in → 2 out4.2473 XPM225 B

Aa2BF2Sr…5aNsentR AYeDqwhg…c64crgqR

249fb2b56e034b…ea9a4985c61354

1 in → 2 out2.2364 XPM226 B

AGXM9uYD…DbiMEF49 AdeTzu3C…JHcawwAA

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.

5.320 × 10⁹⁴(95-digit number)

53205239690584405808…87703349353680557439

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

5.320 × 10⁹⁴(95-digit number)

53205239690584405808…87703349353680557439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.320 × 10⁹⁴(95-digit number)

53205239690584405808…87703349353680557441

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

1.064 × 10⁹⁵(96-digit number)

10641047938116881161…75406698707361114879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.064 × 10⁹⁵(96-digit number)

10641047938116881161…75406698707361114881

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

2.128 × 10⁹⁵(96-digit number)

21282095876233762323…50813397414722229759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.128 × 10⁹⁵(96-digit number)

21282095876233762323…50813397414722229761

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

4.256 × 10⁹⁵(96-digit number)

42564191752467524646…01626794829444459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.256 × 10⁹⁵(96-digit number)

42564191752467524646…01626794829444459521

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

8.512 × 10⁹⁵(96-digit number)

85128383504935049293…03253589658888919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.512 × 10⁹⁵(96-digit number)

85128383504935049293…03253589658888919041

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 #530,813

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