Block #244,299

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 6:54:03 PM · Difficulty 9.9628 · 6,587,076 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97874803419d1a1e390b7b33aca9f387852e58bd4c08586f711b1e3ad4afc8ee

View on Chainz ↗

Height

#244,299

Difficulty

9.962787

Transactions

Size

2.04 KB

Version

Bits

09f67934

Nonce

28,001

Timestamp

11/4/2013, 6:54:03 PM

Confirmations

6,587,076

Mined by

⛏️ KRw;AYdkvntTwj3BnBQaRYHStddbw7TCE18Zvb

Merkle Root

9e3709ad9facb49552af117032d7a8405656c5c0f8f59c3f3c7696900b59bad3

Transactions (1)

Coinbase9e3709ad9facb4…7696900b59bad3

1 in → 57 out10.0207 XPM1.95 KB

AYdkvntT…TCE18Zvb AQtzUSwq…htAuF3yC AZWiC56x…NwextJca AcEnwywz…vZtt2xTs AKDTDDtx…iqvw9cdY

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.

1.054 × 10⁹⁷(98-digit number)

10546356570455338827…66888337303068851199

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

1.054 × 10⁹⁷(98-digit number)

10546356570455338827…66888337303068851199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.054 × 10⁹⁷(98-digit number)

10546356570455338827…66888337303068851201

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

2.109 × 10⁹⁷(98-digit number)

21092713140910677655…33776674606137702399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.109 × 10⁹⁷(98-digit number)

21092713140910677655…33776674606137702401

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

4.218 × 10⁹⁷(98-digit number)

42185426281821355311…67553349212275404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.218 × 10⁹⁷(98-digit number)

42185426281821355311…67553349212275404801

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

8.437 × 10⁹⁷(98-digit number)

84370852563642710622…35106698424550809599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.437 × 10⁹⁷(98-digit number)

84370852563642710622…35106698424550809601

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

1.687 × 10⁹⁸(99-digit number)

16874170512728542124…70213396849101619199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #244,299

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