Block #1,413,827

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2016, 5:15:28 AM · Difficulty 10.7965 · 5,427,404 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a2a9653067daa17e35bdb24fa94f2aed60cdf14835a2309a611cd439af72e8d

View on Chainz ↗

Height

#1,413,827

Difficulty

10.796504

Transactions

Size

662 B

Version

Bits

0acbe7ad

Nonce

2,084,830,554

Timestamp

1/15/2016, 5:15:28 AM

Confirmations

5,427,404

Mined by

⛏️ P2SHAJwTcd12cTQsFCe7AWWtYqg7JwZUXnCuAs

Merkle Root

0f322560f006bbb78e671f9144d9cde2492b228e71340bdaa7c7ecc734a9797b

Transactions (2)

Coinbasee11d2df6747cff…6ab2734c4ca25a

1 in → 1 out8.5800 XPM109 B

AJwTcd12…ZUXnCuAs

2cebcb03e90a1a…a163753c98808a

1 in → 9 out3.5185 XPM463 B

AZiaPpUc…8a6R2ySP AcFf68GJ…soMGkgc2 AZW3MMEU…aAhEF2oW AVjBizVs…tVDrfWHQ AWFzNALq…1tR6n9u8

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.

5.059 × 10⁹³(94-digit number)

50599345880768967627…08573096315459384919

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

5.059 × 10⁹³(94-digit number)

50599345880768967627…08573096315459384919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.059 × 10⁹³(94-digit number)

50599345880768967627…08573096315459384921

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

1.011 × 10⁹⁴(95-digit number)

10119869176153793525…17146192630918769839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.011 × 10⁹⁴(95-digit number)

10119869176153793525…17146192630918769841

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

2.023 × 10⁹⁴(95-digit number)

20239738352307587051…34292385261837539679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.023 × 10⁹⁴(95-digit number)

20239738352307587051…34292385261837539681

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

4.047 × 10⁹⁴(95-digit number)

40479476704615174102…68584770523675079359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.047 × 10⁹⁴(95-digit number)

40479476704615174102…68584770523675079361

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

8.095 × 10⁹⁴(95-digit number)

80958953409230348204…37169541047350158719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.095 × 10⁹⁴(95-digit number)

80958953409230348204…37169541047350158721

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 #1,413,827

Cookie Preferences