Block #518,718

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 6:55:23 PM · Difficulty 10.8539 · 6,287,294 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05ada0df1f817ff8021eb68cd897719152c8723bdd90e32d11a1b89072ccedde

View on Chainz ↗

Height

#518,718

Difficulty

10.853947

Transactions

Size

1.25 KB

Version

Bits

0ada9c3e

Nonce

139,810,399

Timestamp

4/30/2014, 6:55:23 PM

Confirmations

6,287,294

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3ad3237fec472261ea2f65a5773e1a5092e546a65be3c498fbf2d33a44dbfc12

Transactions (3)

Coinbase11a1a6e50f489e…6d3684dfe3c6f9

1 in → 1 out8.4900 XPM116 B

AbwWkWZt…kawDhufa

78aac93db1a6bb…cbbdbd0feafea3

4 in → 11 out34.0200 XPM843 B

AVnwwmh8…r1rYV3zC AZwXBq4j…rzStTzBk ALHBdz1N…v6hU6ZDR Ae6erKQZ…ETXdnGpE AXDEZh15…FbrAPGkC

d00f8cd71763fc…8f077de41e0d50

1 in → 2 out6.4210 XPM226 B

ATeh8NY7…suX539WX ASDFz8h9…R5bQUdDw

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.

2.291 × 10¹⁰⁰(101-digit number)

22911992897040444958…64820147775861370879

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

2.291 × 10¹⁰⁰(101-digit number)

22911992897040444958…64820147775861370879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.291 × 10¹⁰⁰(101-digit number)

22911992897040444958…64820147775861370881

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

4.582 × 10¹⁰⁰(101-digit number)

45823985794080889917…29640295551722741759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.582 × 10¹⁰⁰(101-digit number)

45823985794080889917…29640295551722741761

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

9.164 × 10¹⁰⁰(101-digit number)

91647971588161779835…59280591103445483519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.164 × 10¹⁰⁰(101-digit number)

91647971588161779835…59280591103445483521

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

1.832 × 10¹⁰¹(102-digit number)

18329594317632355967…18561182206890967039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.832 × 10¹⁰¹(102-digit number)

18329594317632355967…18561182206890967041

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

3.665 × 10¹⁰¹(102-digit number)

36659188635264711934…37122364413781934079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.665 × 10¹⁰¹(102-digit number)

36659188635264711934…37122364413781934081

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