Block #83,753

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/26/2013, 8:50:23 AM · Difficulty 9.2706 · 6,728,783 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53d091d8bc4683cc80081616a3708f022dd887e89ee289ea6fe9af476c3d2cc3

View on Chainz ↗

Height

#83,753

Difficulty

9.270584

Transactions

Size

660 B

Version

Bits

094544fd

Nonce

10,029

Timestamp

7/26/2013, 8:50:23 AM

Confirmations

6,728,783

Mined by

⛏️ P2SHAW22zUZx11iq68jZLRopJbWczmpV9NoVr7

Merkle Root

f415f488dba8e2183600c2dc8a15c62f6f88017ec8e5c75de9896f5eac292eb5

Transactions (3)

Coinbase5b12dd073eb072…63a87a4acaf33a

1 in → 1 out11.6600 XPM110 B

AW22zUZx…pV9NoVr7

92fa96903faf4d…a440e2a37438ac

1 in → 2 out1.4750 XPM227 B

Abt6m5Vm…tqCHDKTF AcWYJrus…fextne2J

ccd764f5d0df4b…aed925917c1431

1 in → 2 out0.0300 XPM225 B

AXFvPnxx…DHvoX6xX AP3yphZq…o29fk4eW

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.

1.130 × 10¹¹⁴(115-digit number)

11302039337535616695…28582205982039676939

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

1.130 × 10¹¹⁴(115-digit number)

11302039337535616695…28582205982039676939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.130 × 10¹¹⁴(115-digit number)

11302039337535616695…28582205982039676941

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

2.260 × 10¹¹⁴(115-digit number)

22604078675071233390…57164411964079353879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.260 × 10¹¹⁴(115-digit number)

22604078675071233390…57164411964079353881

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

4.520 × 10¹¹⁴(115-digit number)

45208157350142466780…14328823928158707759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.520 × 10¹¹⁴(115-digit number)

45208157350142466780…14328823928158707761

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

9.041 × 10¹¹⁴(115-digit number)

90416314700284933561…28657647856317415519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.041 × 10¹¹⁴(115-digit number)

90416314700284933561…28657647856317415521

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

1.808 × 10¹¹⁵(116-digit number)

18083262940056986712…57315295712634831039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #83,753

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