Block #289,736

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 8:36:39 AM · Difficulty 9.9887 · 6,525,213 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ea6b5f714cf696c6bbfca7b7d4d66545692316560273831147ec497e0a4e0a2

View on Chainz ↗

Height

#289,736

Difficulty

9.988739

Transactions

Size

1.77 KB

Version

Bits

09fd1df8

Nonce

131,471

Timestamp

12/2/2013, 8:36:39 AM

Confirmations

6,525,213

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

588a43cc8f67b61d68464f81e916557642d8c01a3d1233cce485b3b9087fe7d4

Transactions (5)

Coinbaseb9be54e6c50488…0d74af77a9273f

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

2cec3cae5345f1…3fe08974c5cfa9

2 in → 7 out20.0100 XPM477 B

AJzotVt1…n2DypEMR AHprswVT…7ysvGhPF AeKNrjNj…1NEq95Ta AKgSdxx4…xguBFE3e ASWp6454…JFPEKgqq

04928f411ccfa7…dccd709ad7e5ba

1 in → 5 out63.9600 XPM329 B

AWt2msfW…NMbfwXVQ AZ1BTjCh…JnBxH9Dq AegEGk5u…c5AnQ1n3 AHoENRJk…NhmYqijD ANJdMKYn…vtC21rPz

7747076f4715ad…8742d213d58282

1 in → 5 out55.9500 XPM328 B

AWt2msfW…NMbfwXVQ AZ1BTjCh…JnBxH9Dq Aan4DcVK…C9nm2g91 AegEGk5u…c5AnQ1n3 AHoENRJk…NhmYqijD

2b406b56d2e7d1…95590b2e0ed66e

2 in → 5 out9.7399 XPM475 B

AZBpndYh…aihvEhz4 AHoENRJk…NhmYqijD AegEGk5u…c5AnQ1n3 AWt2msfW…NMbfwXVQ AZ1BTjCh…JnBxH9Dq

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.

3.005 × 10⁹⁶(97-digit number)

30053387848512516329…55978425218918463039

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

3.005 × 10⁹⁶(97-digit number)

30053387848512516329…55978425218918463039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.005 × 10⁹⁶(97-digit number)

30053387848512516329…55978425218918463041

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

6.010 × 10⁹⁶(97-digit number)

60106775697025032658…11956850437836926079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.010 × 10⁹⁶(97-digit number)

60106775697025032658…11956850437836926081

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

1.202 × 10⁹⁷(98-digit number)

12021355139405006531…23913700875673852159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.202 × 10⁹⁷(98-digit number)

12021355139405006531…23913700875673852161

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

2.404 × 10⁹⁷(98-digit number)

24042710278810013063…47827401751347704319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.404 × 10⁹⁷(98-digit number)

24042710278810013063…47827401751347704321

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

4.808 × 10⁹⁷(98-digit number)

48085420557620026127…95654803502695408639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.808 × 10⁹⁷(98-digit number)

48085420557620026127…95654803502695408641

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

Block #289,736

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