Block #1,522,028

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2016, 8:02:29 PM · Difficulty 10.5932 · 5,304,086 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

36e0d447e87dfde7cfb8771cfd9f9d81b7bf5a6698f64887357c1a6ff7c4b355

View on Chainz ↗

Height

#1,522,028

Difficulty

10.593198

Transactions

Size

1.31 KB

Version

Bits

0a97dbcd

Nonce

1,150,517,159

Timestamp

4/1/2016, 8:02:29 PM

Confirmations

5,304,086

Mined by

⛏️ P2SHAGMc3dGx56omoQSbLcZKB3eyDUN4g4GNM2

Merkle Root

21d5ae933da5af448ae910302a61f699d968855c2d0f564840da8d1a79366582

Transactions (2)

Coinbase1a5d25b6ef9cd4…3606f3b04578b3

1 in → 1 out8.9200 XPM109 B

AGMc3dGx…N4g4GNM2

6a6b0fa70ad8b9…fbb8bfaa000aef

1 in → 29 out102.7003 XPM1.12 KB

Adh1zP7M…SBrHU6uw AMQvxBuX…wTpqo2Na Adbk1uap…qUZNwEcG AYWLC16C…TkaxxAx8 ASG21nzq…iMYaGLq3

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.

3.169 × 10⁹⁷(98-digit number)

31694565524159493801…26043474769863802879

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

3.169 × 10⁹⁷(98-digit number)

31694565524159493801…26043474769863802879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.169 × 10⁹⁷(98-digit number)

31694565524159493801…26043474769863802881

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

6.338 × 10⁹⁷(98-digit number)

63389131048318987603…52086949539727605759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.338 × 10⁹⁷(98-digit number)

63389131048318987603…52086949539727605761

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

1.267 × 10⁹⁸(99-digit number)

12677826209663797520…04173899079455211519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.267 × 10⁹⁸(99-digit number)

12677826209663797520…04173899079455211521

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

2.535 × 10⁹⁸(99-digit number)

25355652419327595041…08347798158910423039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.535 × 10⁹⁸(99-digit number)

25355652419327595041…08347798158910423041

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

5.071 × 10⁹⁸(99-digit number)

50711304838655190082…16695596317820846079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.071 × 10⁹⁸(99-digit number)

50711304838655190082…16695596317820846081

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 #1,522,028

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