Block #820,865

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/21/2014, 2:51:56 AM · Difficulty 10.9768 · 5,989,758 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

28f7f08ca116d98a8e388b512d94666e3ce0f476025d9b51395e607b6d99ad00

View on Chainz ↗

Height

#820,865

Difficulty

10.976765

Transactions

Size

1.52 KB

Version

Bits

0afa0d3d

Nonce

1,121,256,308

Timestamp

11/21/2014, 2:51:56 AM

Confirmations

5,989,758

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1fa32d83a92434c301ac7f067a50a4035b5d70cc768a3cb67e8a48146b7d6418

Transactions (5)

Coinbasecfb794dcef43e3…16cf9d0c9b50e9

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

ea8f280ae855ab…b878969e0dbf5c

1 in → 2 out8.2800 XPM226 B

AYnFsFNf…Fwq2M8DQ Acibz2hH…4KK9AWqC

1913412e334673…5cd244e8262fde

1 in → 2 out8.2800 XPM225 B

AVLfeidA…WsPVUY18 AMoJsji6…a13Bp22Q

c266865bfbc969…f8f2436890385d

1 in → 2 out8.2800 XPM226 B

AGdWVjRk…LFVsqCnK AHhmLuCH…Qry1zFJ7

84138c33502cb9…22473cd6f72c7d

4 in → 2 out25.2467 XPM670 B

Aefar4Yh…sDSttbrX AbreMMbU…9yQCEF7B

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.

4.994 × 10⁹⁶(97-digit number)

49946636860803987316…10109522027880953599

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

4.994 × 10⁹⁶(97-digit number)

49946636860803987316…10109522027880953599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.994 × 10⁹⁶(97-digit number)

49946636860803987316…10109522027880953601

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

9.989 × 10⁹⁶(97-digit number)

99893273721607974633…20219044055761907199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.989 × 10⁹⁶(97-digit number)

99893273721607974633…20219044055761907201

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

1.997 × 10⁹⁷(98-digit number)

19978654744321594926…40438088111523814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.997 × 10⁹⁷(98-digit number)

19978654744321594926…40438088111523814401

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

3.995 × 10⁹⁷(98-digit number)

39957309488643189853…80876176223047628799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.995 × 10⁹⁷(98-digit number)

39957309488643189853…80876176223047628801

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

7.991 × 10⁹⁷(98-digit number)

79914618977286379706…61752352446095257599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.991 × 10⁹⁷(98-digit number)

79914618977286379706…61752352446095257601

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

1.598 × 10⁹⁸(99-digit number)

15982923795457275941…23504704892190515199

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 #820,865

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