Block #1,525,808

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2016, 9:06:48 AM · Difficulty 10.6027 · 5,287,079 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9d91bc93c5beca64da09c8c77aa5ab833d75743ac514ef3a550f6756f043fb2

View on Chainz ↗

Height

#1,525,808

Difficulty

10.602671

Transactions

Size

1.38 KB

Version

Bits

0a9a48a4

Nonce

1,732,223,374

Timestamp

4/4/2016, 9:06:48 AM

Confirmations

5,287,079

Mined by

⛏️ P2SHAG7ypzTbbaf9DPtJqPVvgkcfBGu1AWoTGq

Merkle Root

de02d53469384daa9890db84bb996e2584f8a2eed6749f3a716a3d33fd4d3b06

Transactions (2)

Coinbase070d5fa4425db2…ab0e67311ec822

1 in → 1 out8.9000 XPM110 B

AG7ypzTb…u1AWoTGq

b7a9abc01e1f42…41e477ac7250ee

1 in → 31 out48.4581 XPM1.18 KB

ATyyatFN…YMychM5g AHLrfMCb…5eE2yTTn ANompeRr…MGyNnrFD ARbmELZZ…D2EmA9eK ARPpsWhQ…ExypM2rQ

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.

1.964 × 10⁹⁵(96-digit number)

19644251937220457232…34985213270347987519

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

1.964 × 10⁹⁵(96-digit number)

19644251937220457232…34985213270347987519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.964 × 10⁹⁵(96-digit number)

19644251937220457232…34985213270347987521

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

3.928 × 10⁹⁵(96-digit number)

39288503874440914465…69970426540695975039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.928 × 10⁹⁵(96-digit number)

39288503874440914465…69970426540695975041

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

7.857 × 10⁹⁵(96-digit number)

78577007748881828930…39940853081391950079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.857 × 10⁹⁵(96-digit number)

78577007748881828930…39940853081391950081

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

1.571 × 10⁹⁶(97-digit number)

15715401549776365786…79881706162783900159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.571 × 10⁹⁶(97-digit number)

15715401549776365786…79881706162783900161

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

3.143 × 10⁹⁶(97-digit number)

31430803099552731572…59763412325567800319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.143 × 10⁹⁶(97-digit number)

31430803099552731572…59763412325567800321

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 #1,525,808

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