Block #1,516,936

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2016, 5:28:01 AM · Difficulty 10.6011 · 5,291,727 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5005ef078ae41f0a173254723486b9be459b27eddc9797a9838e901653e45c00

View on Chainz ↗

Height

#1,516,936

Difficulty

10.601137

Transactions

Size

79.50 KB

Version

Bits

0a99e423

Nonce

282,110,929

Timestamp

3/29/2016, 5:28:01 AM

Confirmations

5,291,727

Mined by

⛏️ P2SHANRTk3wGZkF741hUi1Fy1zceahXPxSZbsS

Merkle Root

8d8e81687f33cf59581f2a8ded0c7f009db67a6d277eff7c64eb1acdef5730b7

Transactions (3)

Coinbase41676c996dfba2…349e9751c9fc14

1 in → 1 out9.8600 XPM109 B

ANRTk3wG…XPxSZbsS

3a3f45308b6420…e7fed3a30ef741

15 in → 1 out59.9700 XPM2.21 KB

AQVNVjFK…BBBxJVUq

8ea2d5a144dccc…40284085c06e90

533 in → 1 out50.9097 XPM77.09 KB

AJdM6BQD…g1g59wty

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.

3.791 × 10⁹⁵(96-digit number)

37919177252157785757…88465311072140832959

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

3.791 × 10⁹⁵(96-digit number)

37919177252157785757…88465311072140832959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.791 × 10⁹⁵(96-digit number)

37919177252157785757…88465311072140832961

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

7.583 × 10⁹⁵(96-digit number)

75838354504315571515…76930622144281665919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.583 × 10⁹⁵(96-digit number)

75838354504315571515…76930622144281665921

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

1.516 × 10⁹⁶(97-digit number)

15167670900863114303…53861244288563331839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.516 × 10⁹⁶(97-digit number)

15167670900863114303…53861244288563331841

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

3.033 × 10⁹⁶(97-digit number)

30335341801726228606…07722488577126663679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.033 × 10⁹⁶(97-digit number)

30335341801726228606…07722488577126663681

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

6.067 × 10⁹⁶(97-digit number)

60670683603452457212…15444977154253327359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.067 × 10⁹⁶(97-digit number)

60670683603452457212…15444977154253327361

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 #1,516,936

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