Block #2,415,144

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/8/2017, 6:51:03 PM · Difficulty 10.9044 · 4,416,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e38f797c62f963b55f2ad3e241eb1ea9503c353af836d91536b67193173a9ca

View on Chainz ↗

Height

#2,415,144

Difficulty

10.904404

Transactions

Size

1.15 KB

Version

Bits

0ae786fd

Nonce

447,666,855

Timestamp

12/8/2017, 6:51:03 PM

Confirmations

4,416,580

Mined by

⛏️ P2SHAG3L3Vo71Lzf5tfLmmQuEgTYZSxKg89pmn

Merkle Root

141d33c27b5c49e7aee920c9f8a366c29185ab51c5735e31a19fcbfe8e16211b

Transactions (4)

Coinbase82f10d454a01a1…32928668afa896

1 in → 1 out8.4300 XPM109 B

AG3L3Vo7…xKg89pmn

e10841a09b80f0…6e8f7ad7362cdd

3 in → 2 out0.4839 XPM522 B

AQFCRbM1…2k4tFYQA AGZrmqtP…d7dYqqxq

1f7ccf73ef6ee7…132cd9def1c2dc

1 in → 2 out4.3104 XPM226 B

AWwU4LD8…HHQCgd15 ANxNfXmZ…4p5PaHCM

4914e9d622e083…ddd8a4055d0812

1 in → 2 out4.1200 XPM225 B

AX3rxQXW…r43ypFZx AQxt21E9…7jVMypTq

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.

8.160 × 10⁹⁶(97-digit number)

81601539074350324794…63468213947012976639

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

8.160 × 10⁹⁶(97-digit number)

81601539074350324794…63468213947012976639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.160 × 10⁹⁶(97-digit number)

81601539074350324794…63468213947012976641

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

1.632 × 10⁹⁷(98-digit number)

16320307814870064958…26936427894025953279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.632 × 10⁹⁷(98-digit number)

16320307814870064958…26936427894025953281

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

3.264 × 10⁹⁷(98-digit number)

32640615629740129917…53872855788051906559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.264 × 10⁹⁷(98-digit number)

32640615629740129917…53872855788051906561

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

6.528 × 10⁹⁷(98-digit number)

65281231259480259835…07745711576103813119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.528 × 10⁹⁷(98-digit number)

65281231259480259835…07745711576103813121

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

1.305 × 10⁹⁸(99-digit number)

13056246251896051967…15491423152207626239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.305 × 10⁹⁸(99-digit number)

13056246251896051967…15491423152207626241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.611 × 10⁹⁸(99-digit number)

26112492503792103934…30982846304415252479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,415,144

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