Block #274,997

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 12:33:20 PM · Difficulty 9.9594 · 6,537,826 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abfc67ca4a0fe78339b608be561cc8e0e737e5e08a1031ebed441da82c487341

View on Chainz ↗

Height

#274,997

Difficulty

9.959441

Transactions

Size

2.53 KB

Version

Bits

09f59df4

Nonce

50,347

Timestamp

11/26/2013, 12:33:20 PM

Confirmations

6,537,826

Mined by

⛏️ 52aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

e1f89477e801bd9c6d973de3b3841b6be8e7a0e70ae8b078c3f9fff69775ffa1

Transactions (4)

Coinbasee8ceb4fbea3058…a1de853f0b0056

1 in → 30 out10.0500 XPM1.06 KB

APeshfYV…3PKcKMKH Abv8pzf1…t4zPXDTV AGQxR1oS…2N1xAZXN Ae58nAEb…GFUA15fv AZYSGESK…Wtzbd7bt

2ccf6800ff2796…ba412b673e0235

6 in → 2 out80.7134 XPM967 B

ASu2fkLS…tyEDxwWS AXCZzjVQ…vdk6PoeN

eb1fa7ea6db6df…02e957b4facae7

1 in → 2 out8.0483 XPM226 B

AbHMdna1…hkpEYETK AcuLwgTZ…7wr5z3Ua

d87e9574f0b2b7…00d969bbaf8819

1 in → 2 out2.9238 XPM226 B

AdrVtwNn…qiTgyMPm AJ4Rc3t3…DscKhLrr

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.

3.811 × 10⁹⁴(95-digit number)

38116719157989807303…13521198301258934399

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

3.811 × 10⁹⁴(95-digit number)

38116719157989807303…13521198301258934399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.811 × 10⁹⁴(95-digit number)

38116719157989807303…13521198301258934401

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

7.623 × 10⁹⁴(95-digit number)

76233438315979614606…27042396602517868799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.623 × 10⁹⁴(95-digit number)

76233438315979614606…27042396602517868801

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

1.524 × 10⁹⁵(96-digit number)

15246687663195922921…54084793205035737599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.524 × 10⁹⁵(96-digit number)

15246687663195922921…54084793205035737601

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

3.049 × 10⁹⁵(96-digit number)

30493375326391845842…08169586410071475199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.049 × 10⁹⁵(96-digit number)

30493375326391845842…08169586410071475201

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

6.098 × 10⁹⁵(96-digit number)

60986750652783691684…16339172820142950399

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 #274,997

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