Block #2,874,283

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/9/2018, 5:28:55 PM · Difficulty 11.6632 · 3,959,038 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

438471d16effb982f83c55872f5749cc41dd83f4b1a075fdab13aa2d1d2ca28b

View on Chainz ↗

Height

#2,874,283

Difficulty

11.663178

Transactions

Size

767 B

Version

Bits

0ba9c602

Nonce

1,009,557,387

Timestamp

10/9/2018, 5:28:55 PM

Confirmations

3,959,038

Mined by

⛏️ P2SHAevpYpASsueWtW4Z2iGcckdeg81rfQKJnM

Merkle Root

c1bdc0e42220b44191fa7a2fc06cb87d31906f4900d16231c98fb3b86ac6c75a

Transactions (3)

Coinbase074f15949dc585…5410fdc501dc6c

1 in → 1 out7.3600 XPM109 B

AevpYpAS…1rfQKJnM

275a5c34e2f649…8a16d8446b2feb

2 in → 2 out10.6577 XPM341 B

AVsHz48p…fGrgLUJr AXCGoVa4…4e7qSiHM

cae8752489a425…77e215631670eb

1 in → 2 out1.7921 XPM226 B

AJP6VHgV…DCc6rxzj ARMFdT2w…TGxHik4a

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.

1.727 × 10⁹⁶(97-digit number)

17274023187816355889…81959224998172907519

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

1.727 × 10⁹⁶(97-digit number)

17274023187816355889…81959224998172907519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.727 × 10⁹⁶(97-digit number)

17274023187816355889…81959224998172907521

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

3.454 × 10⁹⁶(97-digit number)

34548046375632711779…63918449996345815039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.454 × 10⁹⁶(97-digit number)

34548046375632711779…63918449996345815041

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

6.909 × 10⁹⁶(97-digit number)

69096092751265423559…27836899992691630079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.909 × 10⁹⁶(97-digit number)

69096092751265423559…27836899992691630081

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

1.381 × 10⁹⁷(98-digit number)

13819218550253084711…55673799985383260159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.381 × 10⁹⁷(98-digit number)

13819218550253084711…55673799985383260161

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

2.763 × 10⁹⁷(98-digit number)

27638437100506169423…11347599970766520319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.763 × 10⁹⁷(98-digit number)

27638437100506169423…11347599970766520321

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

5.527 × 10⁹⁷(98-digit number)

55276874201012338847…22695199941533040639

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 #2,874,283

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