Block #263,913

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/18/2013, 5:55:24 AM · Difficulty 9.9653 · 6,550,565 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3b0ed1aee603e0b8b7d4d00b77a96aefcff7b6ddfbf758b74844ca1f1444cc86

View on Chainz ↗

Height

#263,913

Difficulty

9.965293

Transactions

Size

1.13 KB

Version

Bits

09f71d69

Nonce

47,149

Timestamp

11/18/2013, 5:55:24 AM

Confirmations

6,550,565

Mined by

⛏️ P2SHAGNPrf4Wya2PSBnXmVeYxGwKdBu7DkzwQ8

Merkle Root

ecdc6264a915b51f05a4920b3b6ed34fab2744c0cff7d8720a3c003418c16217

Transactions (3)

Coinbase83d856eb3e7b39…be1822d646298c

1 in → 1 out10.0700 XPM109 B

AGNPrf4W…u7DkzwQ8

42b0700c60fb51…438f823c0dfffd

2 in → 6 out20.0500 XPM441 B

Af5JcoF1…bCtmmgeZ AL7194fk…YNQBVjTB ARm2sREf…CfbJteZy AeKNrjNj…1NEq95Ta AcADmAoe…8iNnoMzB

742ad2fb40d58f…43617b33ca85ee

3 in → 2 out4.2700 XPM520 B

AQyA7HvX…MUGan3Ai AaAcj1Ti…1iuumShZ

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.

2.956 × 10⁹⁰(91-digit number)

29562040898087227551…58896285344718149659

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

2.956 × 10⁹⁰(91-digit number)

29562040898087227551…58896285344718149659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.956 × 10⁹⁰(91-digit number)

29562040898087227551…58896285344718149661

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

5.912 × 10⁹⁰(91-digit number)

59124081796174455102…17792570689436299319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.912 × 10⁹⁰(91-digit number)

59124081796174455102…17792570689436299321

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

1.182 × 10⁹¹(92-digit number)

11824816359234891020…35585141378872598639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.182 × 10⁹¹(92-digit number)

11824816359234891020…35585141378872598641

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

2.364 × 10⁹¹(92-digit number)

23649632718469782040…71170282757745197279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.364 × 10⁹¹(92-digit number)

23649632718469782040…71170282757745197281

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

4.729 × 10⁹¹(92-digit number)

47299265436939564081…42340565515490394559

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 #263,913

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