Block #505,926

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/22/2014, 6:13:27 PM · Difficulty 10.8127 · 6,311,390 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9583d11f59bf06cac4d10757a8fdcb98f625eaf6bb3bae1bfdd7876db26aa759

View on Chainz ↗

Height

#505,926

Difficulty

10.812707

Transactions

Size

1.45 KB

Version

Bits

0ad00d95

Nonce

83,646,838

Timestamp

4/22/2014, 6:13:27 PM

Confirmations

6,311,390

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d223bff29e23359242b1064dfb4d107a93808189437e9842925174269c17fae8

Transactions (4)

Coinbaseaeaa33ea1c2734…b5bd7d083c5469

1 in → 1 out8.5800 XPM116 B

AbwWkWZt…kawDhufa

84daba671ad335…79cd093280f54f

1 in → 2 out3.7241 XPM226 B

AJNDZ5iE…CjAs7JQt AdqH4QjD…3vhGVHG4

d94014d6fb64f2…3da271b7cbe06e

1 in → 2 out1.4517 XPM227 B

AKW81X95…z4YfdXgx APowTn2c…4QDQdRVF

1fc88d4bc56bc0…2afdb43a69b02b

5 in → 2 out1.0241 XPM819 B

AWGSZW6k…RX7ud8SZ AbF9ynWo…iU1WpdUR

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.

2.041 × 10⁹⁸(99-digit number)

20414728147236812362…88702687330380665799

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

2.041 × 10⁹⁸(99-digit number)

20414728147236812362…88702687330380665799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.041 × 10⁹⁸(99-digit number)

20414728147236812362…88702687330380665801

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

4.082 × 10⁹⁸(99-digit number)

40829456294473624724…77405374660761331599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.082 × 10⁹⁸(99-digit number)

40829456294473624724…77405374660761331601

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

8.165 × 10⁹⁸(99-digit number)

81658912588947249449…54810749321522663199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.165 × 10⁹⁸(99-digit number)

81658912588947249449…54810749321522663201

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

1.633 × 10⁹⁹(100-digit number)

16331782517789449889…09621498643045326399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.633 × 10⁹⁹(100-digit number)

16331782517789449889…09621498643045326401

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

3.266 × 10⁹⁹(100-digit number)

32663565035578899779…19242997286090652799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.266 × 10⁹⁹(100-digit number)

32663565035578899779…19242997286090652801

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 #505,926

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