Block #84,820

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 1:46:07 AM · Difficulty 9.2784 · 6,725,564 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77f4a5131e2e3f3a1d2a9a3e49b1f77e9b9bdfaa5cf8d3f97927782cc82de49c

View on Chainz ↗

Height

#84,820

Difficulty

9.278426

Transactions

Size

208 B

Version

Bits

094746e9

Nonce

412

Timestamp

7/27/2013, 1:46:07 AM

Confirmations

6,725,564

Mined by

⛏️ P2SHAMvyXHHsMogVazCkRbFEDuxk36YBhzxSCJ

Merkle Root

cfb138110126ff62fad4a0824f438bf2ff1cabd4b908b5906904c0b809ef557e

Transactions (1)

Coinbasecfb138110126ff…04c0b809ef557e

1 in → 1 out11.6000 XPM110 B

AMvyXHHs…YBhzxSCJ

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.

9.408 × 10¹¹²(113-digit number)

94080033740068003013…31955207742481309729

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

9.408 × 10¹¹²(113-digit number)

94080033740068003013…31955207742481309729

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.408 × 10¹¹²(113-digit number)

94080033740068003013…31955207742481309731

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

1.881 × 10¹¹³(114-digit number)

18816006748013600602…63910415484962619459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.881 × 10¹¹³(114-digit number)

18816006748013600602…63910415484962619461

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

3.763 × 10¹¹³(114-digit number)

37632013496027201205…27820830969925238919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.763 × 10¹¹³(114-digit number)

37632013496027201205…27820830969925238921

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

7.526 × 10¹¹³(114-digit number)

75264026992054402410…55641661939850477839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.526 × 10¹¹³(114-digit number)

75264026992054402410…55641661939850477841

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

1.505 × 10¹¹⁴(115-digit number)

15052805398410880482…11283323879700955679

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 #84,820

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