Block #505,766

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/22/2014, 3:53:55 PM · Difficulty 10.8119 · 6,299,428 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2927d103a231979dd4a40d3ae9a36046f5501dd02ca241b9612d6e117e979e85

View on Chainz ↗

Height

#505,766

Difficulty

10.811889

Transactions

Size

4.67 KB

Version

Bits

0acfd7ed

Nonce

95,699,964

Timestamp

4/22/2014, 3:53:55 PM

Confirmations

6,299,428

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

5a15169027c834765a79019fde48409b198752eb8b6c3b02095fe662331b14ba

Transactions (5)

Coinbase4583d5233adb00…3b984c65e7273b

1 in → 1 out8.6100 XPM116 B

AbwWkWZt…kawDhufa

2fc3474acdc340…1685db15b70a4d

26 in → 1 out9.8637 XPM3.80 KB

AMPRMjEE…DrNwu4Bp

2842fe1c750611…2e6c0f3c00fa9d

1 in → 2 out6.4687 XPM227 B

AZoEnnQD…5GicVHBE AWbTqqbC…82rS3Ko4

e7e77795def19d…cb223a635882ae

1 in → 2 out1.3333 XPM226 B

ATetssdL…YnXBsgqs Aatjfi4Q…22oxfLqM

d6f8c3a1dd2ca1…b3773adea81380

1 in → 2 out2.3554 XPM227 B

AHt2xB4g…TLho1X8P AXnWMH7u…ZSKQmVLj

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.

1.565 × 10⁹⁸(99-digit number)

15654136511054954486…77191732383386661919

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

1.565 × 10⁹⁸(99-digit number)

15654136511054954486…77191732383386661919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.565 × 10⁹⁸(99-digit number)

15654136511054954486…77191732383386661921

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

3.130 × 10⁹⁸(99-digit number)

31308273022109908973…54383464766773323839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.130 × 10⁹⁸(99-digit number)

31308273022109908973…54383464766773323841

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

6.261 × 10⁹⁸(99-digit number)

62616546044219817946…08766929533546647679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.261 × 10⁹⁸(99-digit number)

62616546044219817946…08766929533546647681

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

1.252 × 10⁹⁹(100-digit number)

12523309208843963589…17533859067093295359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.252 × 10⁹⁹(100-digit number)

12523309208843963589…17533859067093295361

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

2.504 × 10⁹⁹(100-digit number)

25046618417687927178…35067718134186590719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.504 × 10⁹⁹(100-digit number)

25046618417687927178…35067718134186590721

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