Block #518,712

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 6:50:12 PM · Difficulty 10.8540 · 6,289,415 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0fe9c32e83fd1510e6318a7351cc45c7db8d04e4f441b67ed064003d3a61182c

View on Chainz ↗

Height

#518,712

Difficulty

10.853971

Transactions

Size

1.09 KB

Version

Bits

0ada9dd8

Nonce

312,341,360

Timestamp

4/30/2014, 6:50:12 PM

Confirmations

6,289,415

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

1c685cca6f0d3fa029b08e283d4200ac639bb3e56f804dbe7dcfc3528f7669b6

Transactions (5)

Coinbase8251741e996495…8ff34a4fcd4098

1 in → 1 out8.5100 XPM116 B

AbwWkWZt…kawDhufa

4d41835af98ad8…d15acdff8c4b07

1 in → 2 out5.9051 XPM226 B

AcxG1Cky…pSg4D8mE AHWQsZeD…TprkHAkz

96666d18cd1a74…bcfd51239ed6a3

1 in → 2 out2.1658 XPM226 B

AG8u7ddV…cU5QJSqk ATkF8n35…xaos6Z6L

913eec7cb633f4…c91540af9a257c

1 in → 2 out4.9441 XPM227 B

ARFv4z6e…wRty3ux1 AS9ZCvju…bu3NEFwZ

50018f5ee2356b…b7c534fc468070

1 in → 2 out0.7523 XPM227 B

ANZUxYNW…P1pZfYxg AMqmW9ND…zGvTMkUH

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.

6.265 × 10⁹⁸(99-digit number)

62655643306773470536…88207776586669711999

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

6.265 × 10⁹⁸(99-digit number)

62655643306773470536…88207776586669711999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.265 × 10⁹⁸(99-digit number)

62655643306773470536…88207776586669712001

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

1.253 × 10⁹⁹(100-digit number)

12531128661354694107…76415553173339423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.253 × 10⁹⁹(100-digit number)

12531128661354694107…76415553173339424001

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

2.506 × 10⁹⁹(100-digit number)

25062257322709388214…52831106346678847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.506 × 10⁹⁹(100-digit number)

25062257322709388214…52831106346678848001

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

5.012 × 10⁹⁹(100-digit number)

50124514645418776429…05662212693357695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.012 × 10⁹⁹(100-digit number)

50124514645418776429…05662212693357696001

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

1.002 × 10¹⁰⁰(101-digit number)

10024902929083755285…11324425386715391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.002 × 10¹⁰⁰(101-digit number)

10024902929083755285…11324425386715392001

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 #518,712

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