Block #290,968

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 10:54:49 PM · Difficulty 9.9896 · 6,510,845 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5b1bc8d92dd8d0997d4fcd42f90017c86d542759febd9be494dab41f5a892cbc

View on Chainz ↗

Height

#290,968

Difficulty

9.989577

Transactions

Size

899 B

Version

Bits

09fd54e9

Nonce

15,526

Timestamp

12/2/2013, 10:54:49 PM

Confirmations

6,510,845

Mined by

⛏️ paR$gANEZwy9tw1DgYw4uGbmja8PNbrE1uf5dKY

Merkle Root

43c199d499554cf78ae3800352403739046a07f1e253e47209f76b451a0a0f1e

Transactions (4)

Coinbasea8afafa9fc5a0c…9bed26567ff54b

1 in → 1 out10.0100 XPM97 B

ANEZwy9t…E1uf5dKY

3ca4d25ccd8526…7288ebb3d1448d

1 in → 4 out10.0200 XPM260 B

AeKNrjNj…1NEq95Ta AVdWpPFc…EBRQUE9w AHCJrZFA…wMKHchRb ANFpe7j9…DDEt116M

94aa7ec758daf9…ae826a5a76d9e1

1 in → 2 out4.9271 XPM226 B

AWX4hzNj…FGEcXyM3 AX4UBQiJ…HHw2s8gh

ae9a468daec054…3af42d3ca123cf

1 in → 2 out4.1536 XPM226 B

AUnXKNnq…V1v8oZzs AQLgQ1R4…YyexwkDf

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.

1.657 × 10⁹⁵(96-digit number)

16574097282747423565…32752015435994494319

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

1.657 × 10⁹⁵(96-digit number)

16574097282747423565…32752015435994494319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.657 × 10⁹⁵(96-digit number)

16574097282747423565…32752015435994494321

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

3.314 × 10⁹⁵(96-digit number)

33148194565494847131…65504030871988988639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.314 × 10⁹⁵(96-digit number)

33148194565494847131…65504030871988988641

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

6.629 × 10⁹⁵(96-digit number)

66296389130989694262…31008061743977977279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.629 × 10⁹⁵(96-digit number)

66296389130989694262…31008061743977977281

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

1.325 × 10⁹⁶(97-digit number)

13259277826197938852…62016123487955954559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.325 × 10⁹⁶(97-digit number)

13259277826197938852…62016123487955954561

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

2.651 × 10⁹⁶(97-digit number)

26518555652395877704…24032246975911909119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.651 × 10⁹⁶(97-digit number)

26518555652395877704…24032246975911909121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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