Block #1,545,685

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2016, 4:36:58 PM · Difficulty 10.6559 · 5,299,614 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

932e1656856c24307c8cd480defe88c273d094f50ff90a4c5def000c556a3aae

View on Chainz ↗

Height

#1,545,685

Difficulty

10.655874

Transactions

Size

1.14 KB

Version

Bits

0aa7e757

Nonce

215,108,923

Timestamp

4/17/2016, 4:36:58 PM

Confirmations

5,299,614

Mined by

⛏️ P2SHAZDnsTi2MGgC9KFNnZ2VTPCrimriknejcQ

Merkle Root

886f21520529727b26990c02eca96b556750322d59b26193790ec01a446fecf2

Transactions (2)

Coinbase384e6348f44a95…9973867cbd71d8

1 in → 1 out8.8000 XPM109 B

AZDnsTi2…riknejcQ

227e70ac0f8214…fb7a5fea2be4e4

6 in → 2 out94.0090 XPM969 B

AT6xucer…3toba8Mw AG88PAGz…uVnnKCu5

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.

9.667 × 10⁹⁵(96-digit number)

96674503907843039354…14693470333678919679

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

9.667 × 10⁹⁵(96-digit number)

96674503907843039354…14693470333678919679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.667 × 10⁹⁵(96-digit number)

96674503907843039354…14693470333678919681

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

1.933 × 10⁹⁶(97-digit number)

19334900781568607870…29386940667357839359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.933 × 10⁹⁶(97-digit number)

19334900781568607870…29386940667357839361

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

3.866 × 10⁹⁶(97-digit number)

38669801563137215741…58773881334715678719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.866 × 10⁹⁶(97-digit number)

38669801563137215741…58773881334715678721

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

7.733 × 10⁹⁶(97-digit number)

77339603126274431483…17547762669431357439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.733 × 10⁹⁶(97-digit number)

77339603126274431483…17547762669431357441

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

1.546 × 10⁹⁷(98-digit number)

15467920625254886296…35095525338862714879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.546 × 10⁹⁷(98-digit number)

15467920625254886296…35095525338862714881

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 #1,545,685

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