Block #274,323

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 6:06:16 AM · Difficulty 9.9570 · 6,533,895 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3db79134b6a37590ada1e8bf01f5f471d036777df249649d1b820f662275c6b

View on Chainz ↗

Height

#274,323

Difficulty

9.957046

Transactions

Size

1.78 KB

Version

Bits

09f500fd

Nonce

18,602

Timestamp

11/26/2013, 6:06:16 AM

Confirmations

6,533,895

Mined by

⛏️ 5AeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

7757a4f6951df687da31de7ab1f9a5da701fbac3c4a2ee7b6bc2f36586286404

Transactions (2)

Coinbase5103589fb7637d…03332fa3986b47

1 in → 1 out10.0900 XPM110 B

AeKNrjNj…1NEq95Ta

ce06ba957881b0…fbd44bee2903ac

10 in → 13 out95.4560 XPM1.59 KB

AMuPGPXT…eMMNvd8v ARtPXKuc…KzX35CG6 AN6q7u2t…2PeYWW7Q AGQ2fgRV…bLy3QAAV AVxiKGog…52BjuTdq

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.

8.657 × 10⁹⁶(97-digit number)

86577670743296325619…05412791670492629999

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

8.657 × 10⁹⁶(97-digit number)

86577670743296325619…05412791670492629999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.657 × 10⁹⁶(97-digit number)

86577670743296325619…05412791670492630001

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

1.731 × 10⁹⁷(98-digit number)

17315534148659265123…10825583340985259999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.731 × 10⁹⁷(98-digit number)

17315534148659265123…10825583340985260001

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

3.463 × 10⁹⁷(98-digit number)

34631068297318530247…21651166681970519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.463 × 10⁹⁷(98-digit number)

34631068297318530247…21651166681970520001

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

6.926 × 10⁹⁷(98-digit number)

69262136594637060495…43302333363941039999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.926 × 10⁹⁷(98-digit number)

69262136594637060495…43302333363941040001

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

1.385 × 10⁹⁸(99-digit number)

13852427318927412099…86604666727882079999

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 #274,323

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