Block #515,673

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/28/2014, 10:30:07 PM · Difficulty 10.8423 · 6,296,791 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

69ea3a436f64af64bfad326d2af4b442199e48e4c8c67cb8b988a74a2854ee93

View on Chainz ↗

Height

#515,673

Difficulty

10.842330

Transactions

Size

1.95 KB

Version

Bits

0ad7a2ee

Nonce

107,819

Timestamp

4/28/2014, 10:30:07 PM

Confirmations

6,296,791

Mined by

⛏️ P2SHASmVbiQC8uTAbz5erexTtAS8AwV32Qop2A

Merkle Root

6b1271abca63e148983673c62b46f9fdb525c4e6152f9aaee63269985f1d7a84

Transactions (5)

Coinbase91734e2afef320…ac80c765d432dc

1 in → 1 out8.5400 XPM109 B

ASmVbiQC…V32Qop2A

6b10bcccb4e8c2…c353436bc63dd8

7 in → 2 out40.0217 XPM1.09 KB

AZPhnfGE…dSv71WHC AWxJyZgd…1yjGniXL

07900e6029ed7a…45dcbc860381ff

1 in → 2 out2.3887 XPM227 B

ATktzYa6…GfYib6BD AcLdTZM2…MEVhbUEQ

60c8ff96aba2cc…22f46e4743c02c

1 in → 2 out1.2777 XPM226 B

AYZEP2e6…KmTVB8FX AWr7QESV…T91HodnJ

31b4ea61b3bf0f…c76bb7893a1b39

1 in → 2 out1.2461 XPM227 B

AYYwATFQ…jS1va8nr AJgccvsf…kBNznesc

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.

2.095 × 10⁹⁸(99-digit number)

20955137802199375493…82484191974421292099

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

2.095 × 10⁹⁸(99-digit number)

20955137802199375493…82484191974421292099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.095 × 10⁹⁸(99-digit number)

20955137802199375493…82484191974421292101

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

4.191 × 10⁹⁸(99-digit number)

41910275604398750986…64968383948842584199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.191 × 10⁹⁸(99-digit number)

41910275604398750986…64968383948842584201

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

8.382 × 10⁹⁸(99-digit number)

83820551208797501972…29936767897685168399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.382 × 10⁹⁸(99-digit number)

83820551208797501972…29936767897685168401

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

1.676 × 10⁹⁹(100-digit number)

16764110241759500394…59873535795370336799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.676 × 10⁹⁹(100-digit number)

16764110241759500394…59873535795370336801

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

3.352 × 10⁹⁹(100-digit number)

33528220483519000789…19747071590740673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.352 × 10⁹⁹(100-digit number)

33528220483519000789…19747071590740673601

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 #515,673

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