Block #802,707

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/8/2014, 1:40:14 PM · Difficulty 10.9758 · 6,014,194 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4f0a4394d53c38178228b502a8a6b0be0860c612582388ff1a66b7a5e0be41ad

View on Chainz ↗

Height

#802,707

Difficulty

10.975824

Transactions

Size

1.01 KB

Version

Bits

0af9cf97

Nonce

1,826,429,930

Timestamp

11/8/2014, 1:40:14 PM

Confirmations

6,014,194

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

02d3e3243c2a29111cd556f72db60019b44daeccfd9f77aa8cc29e14013e4bb0

Transactions (4)

Coinbaseabd52f4198d80d…3bb2fa859a3597

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

4bc926b95c93cb…e23559bcd21227

1 in → 2 out4.0746 XPM226 B

Aba6XLEW…giia6sUh AKLZUc4r…fof6Y56H

42b3cfed198e28…e136e491aa79fa

1 in → 2 out1.6385 XPM227 B

AGdWVjRk…LFVsqCnK AeXjkrc7…ic7gymgF

e49fd75a1d6f44…0deb9db93fe4e2

2 in → 2 out0.6769 XPM374 B

AcF13VDN…m7kAYb78 AMoJsji6…a13Bp22Q

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.

7.502 × 10⁹⁴(95-digit number)

75020831188307652551…07780249249830794079

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

7.502 × 10⁹⁴(95-digit number)

75020831188307652551…07780249249830794079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.502 × 10⁹⁴(95-digit number)

75020831188307652551…07780249249830794081

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

1.500 × 10⁹⁵(96-digit number)

15004166237661530510…15560498499661588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.500 × 10⁹⁵(96-digit number)

15004166237661530510…15560498499661588161

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

3.000 × 10⁹⁵(96-digit number)

30008332475323061020…31120996999323176319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.000 × 10⁹⁵(96-digit number)

30008332475323061020…31120996999323176321

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

6.001 × 10⁹⁵(96-digit number)

60016664950646122041…62241993998646352639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.001 × 10⁹⁵(96-digit number)

60016664950646122041…62241993998646352641

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

1.200 × 10⁹⁶(97-digit number)

12003332990129224408…24483987997292705279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.200 × 10⁹⁶(97-digit number)

12003332990129224408…24483987997292705281

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

2.400 × 10⁹⁶(97-digit number)

24006665980258448816…48967975994585410559

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 #802,707

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