Block #2,833,006

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/10/2018, 11:06:53 AM · Difficulty 11.7148 · 4,006,489 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

320c2078c7dec94974afb166b8f27da4718449a6288fd71598e6b3b745aeb994

View on Chainz ↗

Height

#2,833,006

Difficulty

11.714798

Transactions

Size

1.13 KB

Version

Bits

0bb6fcfe

Nonce

41,845,760

Timestamp

9/10/2018, 11:06:53 AM

Confirmations

4,006,489

Mined by

⛏️ P2SHAYANFVqga6Ynk6X6d7np8pcqFiY46AWj3H

Merkle Root

71c1dbeabeabce90fb8cf0ccc06a595d968c17e803a2511b1966f156a92a71f2

Transactions (4)

Coinbaseade8ed28199f3e…d53a8ee75b7b34

1 in → 1 out7.3000 XPM110 B

AYANFVqg…Y46AWj3H

9afd60f2d2a6da…3531097ee74544

2 in → 2 out14.5300 XPM307 B

AbuT6MtU…SGj6nVSc AW3QZZmg…j2rGjUkp

6e219e63566dee…338fb665b49b2d

2 in → 2 out14.5300 XPM307 B

AQ7S9cWe…rDsLcCRa AX3VdQCd…LqbTuETc

4209f52d3984af…04b48a9da4206c

2 in → 2 out11.8400 XPM341 B

APVKWthF…PMMxwRoz AZbvYRp8…ZYz34A1j

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.

2.801 × 10⁹⁶(97-digit number)

28016849390132302881…36498101834620231679

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

2.801 × 10⁹⁶(97-digit number)

28016849390132302881…36498101834620231679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.801 × 10⁹⁶(97-digit number)

28016849390132302881…36498101834620231681

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

5.603 × 10⁹⁶(97-digit number)

56033698780264605762…72996203669240463359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.603 × 10⁹⁶(97-digit number)

56033698780264605762…72996203669240463361

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

1.120 × 10⁹⁷(98-digit number)

11206739756052921152…45992407338480926719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.120 × 10⁹⁷(98-digit number)

11206739756052921152…45992407338480926721

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

2.241 × 10⁹⁷(98-digit number)

22413479512105842305…91984814676961853439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.241 × 10⁹⁷(98-digit number)

22413479512105842305…91984814676961853441

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

4.482 × 10⁹⁷(98-digit number)

44826959024211684610…83969629353923706879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.482 × 10⁹⁷(98-digit number)

44826959024211684610…83969629353923706881

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

8.965 × 10⁹⁷(98-digit number)

89653918048423369220…67939258707847413759

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 #2,833,006

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