Block #1,520,251

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/31/2016, 3:03:47 PM · Difficulty 10.5901 · 5,306,905 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

102e99ae0473b9f4ac0be8a59edd24bcf4c46407b1c620481a1a23b6042f82a0

View on Chainz ↗

Height

#1,520,251

Difficulty

10.590083

Transactions

Size

1.25 KB

Version

Bits

0a970fa9

Nonce

197,485,934

Timestamp

3/31/2016, 3:03:47 PM

Confirmations

5,306,905

Mined by

⛏️ P2SHAVQDpV3bKYNFokdFbsJaNX3VDWJkicNBra

Merkle Root

01c5b322df54e249e0a9be2d00eef575eb6f6a3c1617118e3c412cf3ceb6f141

Transactions (2)

Coinbase94c8ae2fd48df8…0871c908a0acee

1 in → 1 out8.9200 XPM109 B

AVQDpV3b…JkicNBra

a35ae7d8a8a465…c21dd4d0deadc5

1 in → 27 out126.8633 XPM1.05 KB

AXWJqtt6…gihu42Qs ASDswapN…8S9rwyc3 AWz1KjjL…8TzR4rmg AZnGyJk4…EJdJG43y AJrpEg1W…koapTd3C

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.

2.416 × 10⁹⁴(95-digit number)

24163074957371175433…59621121129660567259

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

2.416 × 10⁹⁴(95-digit number)

24163074957371175433…59621121129660567259

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.416 × 10⁹⁴(95-digit number)

24163074957371175433…59621121129660567261

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

4.832 × 10⁹⁴(95-digit number)

48326149914742350866…19242242259321134519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.832 × 10⁹⁴(95-digit number)

48326149914742350866…19242242259321134521

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

9.665 × 10⁹⁴(95-digit number)

96652299829484701732…38484484518642269039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.665 × 10⁹⁴(95-digit number)

96652299829484701732…38484484518642269041

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

1.933 × 10⁹⁵(96-digit number)

19330459965896940346…76968969037284538079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.933 × 10⁹⁵(96-digit number)

19330459965896940346…76968969037284538081

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

3.866 × 10⁹⁵(96-digit number)

38660919931793880693…53937938074569076159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.866 × 10⁹⁵(96-digit number)

38660919931793880693…53937938074569076161

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 #1,520,251

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