Block #543,888

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2014, 3:08:10 PM · Difficulty 10.9489 · 6,281,828 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

048be4217893fd422e6e577e01c871e6e37c3e2aa434686ce5f47e12bd3f1a0d

View on Chainz ↗

Height

#543,888

Difficulty

10.948883

Transactions

Size

1.08 KB

Version

Bits

0af2ea00

Nonce

635,930,948

Timestamp

5/14/2014, 3:08:10 PM

Confirmations

6,281,828

Mined by

⛏️ P2SHATW6RN1yStiCqg31fqQPv37PWopK8Z7baw

Merkle Root

f222c6391f57627c7469b0518515ffdc819a4b66a86d02c5c28d5d959f974f6d

Transactions (5)

Coinbasef66a620ef30194…10eca3c719a922

1 in → 1 out8.3700 XPM110 B

ATW6RN1y…pK8Z7baw

d3c567593ac3fe…39a613d023e7be

1 in → 2 out6.0951 XPM225 B

AGdWVjRk…LFVsqCnK AP6WLfPn…DMPoHFdf

657880858565fd…e4db712f7e5dde

1 in → 2 out3.9316 XPM225 B

ATTj3Quj…RogtXXPS AbqVdcFs…Gh7fCqkj

fdb3e5aacffee5…32c7a45e36c009

1 in → 2 out2.2781 XPM225 B

AGAtpNwb…DApoK3RL AKVCZiaN…3Y3mVeg1

f0e6d211a1bf56…3cc15eec13b6a2

1 in → 2 out5.8310 XPM226 B

ASAk5QVj…qmoG5526 AeWYz9nF…7DXcPc8R

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.

7.712 × 10⁹⁶(97-digit number)

77128777915608165973…59760538392025011199

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

7.712 × 10⁹⁶(97-digit number)

77128777915608165973…59760538392025011199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.712 × 10⁹⁶(97-digit number)

77128777915608165973…59760538392025011201

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

1.542 × 10⁹⁷(98-digit number)

15425755583121633194…19521076784050022399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.542 × 10⁹⁷(98-digit number)

15425755583121633194…19521076784050022401

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

3.085 × 10⁹⁷(98-digit number)

30851511166243266389…39042153568100044799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.085 × 10⁹⁷(98-digit number)

30851511166243266389…39042153568100044801

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

6.170 × 10⁹⁷(98-digit number)

61703022332486532779…78084307136200089599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.170 × 10⁹⁷(98-digit number)

61703022332486532779…78084307136200089601

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

1.234 × 10⁹⁸(99-digit number)

12340604466497306555…56168614272400179199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.234 × 10⁹⁸(99-digit number)

12340604466497306555…56168614272400179201

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 #543,888

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