Block #1,525,263

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2016, 12:03:45 AM · Difficulty 10.6024 · 5,284,891 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4cebfbfd0d2e5bfc834f495caa96ad7f78f5d86c1723911a41a0ba4411bd277f

View on Chainz ↗

Height

#1,525,263

Difficulty

10.602393

Transactions

Size

6.46 KB

Version

Bits

0a9a3670

Nonce

657,518,305

Timestamp

4/4/2016, 12:03:45 AM

Confirmations

5,284,891

Mined by

⛏️ P2SHAHwLZg5CaUtgc6JMt63kGk14Us5UBF78Qe

Merkle Root

3845568dd5bc674c789511e5c54f26b508dab698b11d4fd369540ef9465f3ce4

Transactions (5)

Coinbase198cc55fc1aa90…0212a319827ee5

1 in → 1 out8.9500 XPM110 B

AHwLZg5C…5UBF78Qe

2170a9b0879a65…1b04c6fcb2e9b9

1 in → 45 out88.1697 XPM1.65 KB

AWRLz3q4…8hRdTreT AYYBSUVc…UmYHwzfJ AXn94E9d…xKzG1Yrs AaJFayiS…Rv99ip1d AbAeLf91…pT1FwkCX

d4329a8c5be648…32d4a9143977d8

1 in → 51 out7.5468 XPM1.85 KB

APKH9RPe…LUEGiGj5 AZ3cZHxS…1qdoLqba ANinwaYj…hHUWCvDR Acr54Uhg…FeYtSbEq APMuRBbN…ebDYT21o

1590cc46104acf…77eebd9ad68cfb

1 in → 23 out54.9653 XPM939 B

AHLkr8VW…72s1bCzw AJRpsnNi…HqGPsNv4 AekcNWLi…P9WpHDPV AQ8PLTr2…wTMYrCSV APM8ptnq…r5hdjtZo

3df49fe66d5a34…969befda8491e5

1 in → 51 out2.9143 XPM1.85 KB

AS8dnJS7…h6FNYoqm Abf9bYnS…8bmRPE4d AQJ84KY9…mh2qi8M6 AKcXipHk…FMbCb9Jx AVrYghAt…FcSHW68K

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.

8.788 × 10⁹⁶(97-digit number)

87881759744865945523…24267107831169576959

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

8.788 × 10⁹⁶(97-digit number)

87881759744865945523…24267107831169576959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.788 × 10⁹⁶(97-digit number)

87881759744865945523…24267107831169576961

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

1.757 × 10⁹⁷(98-digit number)

17576351948973189104…48534215662339153919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.757 × 10⁹⁷(98-digit number)

17576351948973189104…48534215662339153921

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

3.515 × 10⁹⁷(98-digit number)

35152703897946378209…97068431324678307839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.515 × 10⁹⁷(98-digit number)

35152703897946378209…97068431324678307841

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

7.030 × 10⁹⁷(98-digit number)

70305407795892756419…94136862649356615679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.030 × 10⁹⁷(98-digit number)

70305407795892756419…94136862649356615681

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

1.406 × 10⁹⁸(99-digit number)

14061081559178551283…88273725298713231359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.406 × 10⁹⁸(99-digit number)

14061081559178551283…88273725298713231361

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 #1,525,263

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