Block #296,664

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 3:45:30 AM · Difficulty 9.9918 · 6,516,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93906eeef35c49b6b3eaa5c3b53e5d97d4eea174c1152bd0321ea2d720024ca8

View on Chainz ↗

Height

#296,664

Difficulty

9.991763

Transactions

Size

2.24 KB

Version

Bits

09fde430

Nonce

88,131

Timestamp

12/6/2013, 3:45:30 AM

Confirmations

6,516,289

Mined by

⛏️ aRI;APeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

fd550af7dbc127bfcb2ab029e89b6e0b3efbf65cd5c03f2e81e348675f738813

Transactions (4)

Coinbasecb5690281b666c…b91cd25e30005c

1 in → 30 out9.9800 XPM1.06 KB

APeshfYV…3PKcKMKH AKEwr54i…9BfmMkRh Aeev9L83…xS7WQJRc AJDS4fnU…q3A7F2Eu Ab5zCZXa…CLDccFx6

eebc34b557aa6f…604c70b85474a8

4 in → 2 out15.0725 XPM670 B

AT5oTsET…Pi5H6raU ANwhXTWo…Z7iEnrqu

a7cc22dd6bb200…04e56042ca0144

1 in → 2 out3.5273 XPM227 B

ATstaHZe…zgEmBPPu AGKQpcF3…7uua1tAn

21dc3538cebdbe…ca5e41591e3b28

1 in → 2 out2.7986 XPM225 B

AMWhfZow…EH5vsb34 AdAsi8o5…Umpzw3j2

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.

4.603 × 10⁹⁷(98-digit number)

46034264130965581638…65550475757145006079

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

4.603 × 10⁹⁷(98-digit number)

46034264130965581638…65550475757145006079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.603 × 10⁹⁷(98-digit number)

46034264130965581638…65550475757145006081

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

9.206 × 10⁹⁷(98-digit number)

92068528261931163277…31100951514290012159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.206 × 10⁹⁷(98-digit number)

92068528261931163277…31100951514290012161

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

1.841 × 10⁹⁸(99-digit number)

18413705652386232655…62201903028580024319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.841 × 10⁹⁸(99-digit number)

18413705652386232655…62201903028580024321

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

3.682 × 10⁹⁸(99-digit number)

36827411304772465310…24403806057160048639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.682 × 10⁹⁸(99-digit number)

36827411304772465310…24403806057160048641

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

7.365 × 10⁹⁸(99-digit number)

73654822609544930621…48807612114320097279

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 #296,664

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