Block #2,098,488

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2017, 3:37:43 PM · Difficulty 10.8637 · 4,741,947 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c263b2247ef123108db562c7942ce1fea48f43f6e860cb704c470c553f7419d2

View on Chainz ↗

Height

#2,098,488

Difficulty

10.863735

Transactions

Size

425 B

Version

Bits

0add1dbc

Nonce

667,916,871

Timestamp

5/3/2017, 3:37:43 PM

Confirmations

4,741,947

Mined by

⛏️ P2SHATMSWsRb7UsRER7dRr7nkMgHK9WKzni4fR

Merkle Root

24cc8f7096777f5cc61ed3cd94cf0c89423d45256874af1dd4b165eb8b131c6e

Transactions (2)

Coinbaseafbd7d72d4b149…0548f9f7cd287c

1 in → 1 out8.4700 XPM109 B

ATMSWsRb…WKzni4fR

5b8882fc36ecf6…9ebd948fa93666

1 in → 2 out64.7200 XPM225 B

AWFBSKPQ…ci3y94Wu AbEaSQih…UTYPgxev

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.

3.260 × 10⁹⁶(97-digit number)

32604613927366938701…31110731737395363839

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

3.260 × 10⁹⁶(97-digit number)

32604613927366938701…31110731737395363839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.260 × 10⁹⁶(97-digit number)

32604613927366938701…31110731737395363841

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

6.520 × 10⁹⁶(97-digit number)

65209227854733877403…62221463474790727679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.520 × 10⁹⁶(97-digit number)

65209227854733877403…62221463474790727681

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

1.304 × 10⁹⁷(98-digit number)

13041845570946775480…24442926949581455359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.304 × 10⁹⁷(98-digit number)

13041845570946775480…24442926949581455361

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

2.608 × 10⁹⁷(98-digit number)

26083691141893550961…48885853899162910719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.608 × 10⁹⁷(98-digit number)

26083691141893550961…48885853899162910721

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

5.216 × 10⁹⁷(98-digit number)

52167382283787101922…97771707798325821439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.216 × 10⁹⁷(98-digit number)

52167382283787101922…97771707798325821441

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,098,488

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