Block #513,118

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2014, 7:53:21 AM · Difficulty 10.8346 · 6,296,848 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0b48942fa2ca721611f0f0d5e52ce84706c8e652da0fc778467cec14cecddf9

View on Chainz ↗

Height

#513,118

Difficulty

10.834578

Transactions

Size

891 B

Version

Bits

0ad5a6e1

Nonce

114,785

Timestamp

4/27/2014, 7:53:21 AM

Confirmations

6,296,848

Mined by

⛏️ ^aS\AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

6d8b579d7b58220442b7204f314161fd48f85fe35cd59ae0181cedc503e59a22

Transactions (2)

Coinbasecf66629905aff5…760de7cbdc3e5d

1 in → 15 out8.5100 XPM573 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

05938f39f74119…cc8b94b64f8a1a

1 in → 2 out7.5096 XPM227 B

ALQRpecD…CdCxCEBq AYYwATFQ…jS1va8nr

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.

1.031 × 10⁹⁷(98-digit number)

10310340007254127026…04473926311539237119

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

1.031 × 10⁹⁷(98-digit number)

10310340007254127026…04473926311539237119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.031 × 10⁹⁷(98-digit number)

10310340007254127026…04473926311539237121

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

2.062 × 10⁹⁷(98-digit number)

20620680014508254053…08947852623078474239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.062 × 10⁹⁷(98-digit number)

20620680014508254053…08947852623078474241

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

4.124 × 10⁹⁷(98-digit number)

41241360029016508106…17895705246156948479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.124 × 10⁹⁷(98-digit number)

41241360029016508106…17895705246156948481

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

8.248 × 10⁹⁷(98-digit number)

82482720058033016212…35791410492313896959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.248 × 10⁹⁷(98-digit number)

82482720058033016212…35791410492313896961

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

1.649 × 10⁹⁸(99-digit number)

16496544011606603242…71582820984627793919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.649 × 10⁹⁸(99-digit number)

16496544011606603242…71582820984627793921

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 #513,118

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