Block #515,219

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/28/2014, 3:58:17 PM · Difficulty 10.8402 · 6,291,011 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

afc48fe68467bd88dcaa7dcc0d80fda0316bcd6b25f9e0db1b968d987c6c9ee1

View on Chainz ↗

Height

#515,219

Difficulty

10.840222

Transactions

Size

957 B

Version

Bits

0ad718cb

Nonce

11,372,089

Timestamp

4/28/2014, 3:58:17 PM

Confirmations

6,291,011

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0fb11bf9975555de2398a862ecd194a83b8446c39b96bcea4b54525b04c34cb4

Transactions (3)

Coinbaseb0b2b76455ba32…48ac558585b073

1 in → 1 out8.5200 XPM116 B

AbwWkWZt…kawDhufa

6e556c8db4ed87…09ed1d9a15cabb

3 in → 2 out6.0846 XPM523 B

AeAUP6Yb…52wERAAN ALWv2AoR…r6oW7RQZ

2f93e6f008ddb7…ef33f38977079b

1 in → 2 out4.6066 XPM226 B

AUA9WhWB…6dPD2p3u AS9ZCvju…bu3NEFwZ

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.

2.649 × 10⁹⁸(99-digit number)

26497816067927129625…20337265621359438119

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

2.649 × 10⁹⁸(99-digit number)

26497816067927129625…20337265621359438119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.649 × 10⁹⁸(99-digit number)

26497816067927129625…20337265621359438121

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

5.299 × 10⁹⁸(99-digit number)

52995632135854259250…40674531242718876239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.299 × 10⁹⁸(99-digit number)

52995632135854259250…40674531242718876241

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

1.059 × 10⁹⁹(100-digit number)

10599126427170851850…81349062485437752479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.059 × 10⁹⁹(100-digit number)

10599126427170851850…81349062485437752481

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

2.119 × 10⁹⁹(100-digit number)

21198252854341703700…62698124970875504959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.119 × 10⁹⁹(100-digit number)

21198252854341703700…62698124970875504961

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

4.239 × 10⁹⁹(100-digit number)

42396505708683407400…25396249941751009919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.239 × 10⁹⁹(100-digit number)

42396505708683407400…25396249941751009921

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