Block #502,968

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2014, 6:46:13 PM · Difficulty 10.8082 · 6,313,954 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bbc172ef8ce62d7a4e1621b705d254d07fb0794e2d96700c1d0e7bfea4df5a0f

View on Chainz ↗

Height

#502,968

Difficulty

10.808174

Transactions

Size

436 B

Version

Bits

0acee47b

Nonce

134,774

Timestamp

4/20/2014, 6:46:13 PM

Confirmations

6,313,954

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

cb5d52c8eb21f54cd57827eb66bf85a08c6da23bd5c229f50f8cb0a30a8727e6

Transactions (2)

Coinbase5e901fc8d10834…a7ee153c8f94a7

1 in → 1 out8.5600 XPM116 B

AbwWkWZt…kawDhufa

94dbdb596b6b24…ddc73dbd0558e5

1 in → 2 out0.5974 XPM227 B

AM8GuxnN…AfjbhWoV AY87bah3…ELHLWL4p

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.

1.596 × 10¹⁰¹(102-digit number)

15963268095464917029…04876747379462103039

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

1.596 × 10¹⁰¹(102-digit number)

15963268095464917029…04876747379462103039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.596 × 10¹⁰¹(102-digit number)

15963268095464917029…04876747379462103041

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

3.192 × 10¹⁰¹(102-digit number)

31926536190929834058…09753494758924206079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.192 × 10¹⁰¹(102-digit number)

31926536190929834058…09753494758924206081

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

6.385 × 10¹⁰¹(102-digit number)

63853072381859668117…19506989517848412159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.385 × 10¹⁰¹(102-digit number)

63853072381859668117…19506989517848412161

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

1.277 × 10¹⁰²(103-digit number)

12770614476371933623…39013979035696824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.277 × 10¹⁰²(103-digit number)

12770614476371933623…39013979035696824321

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

2.554 × 10¹⁰²(103-digit number)

25541228952743867246…78027958071393648639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.554 × 10¹⁰²(103-digit number)

25541228952743867246…78027958071393648641

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 #502,968

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