Block #1,477,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/29/2016, 8:04:43 PM · Difficulty 10.7050 · 5,339,081 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

14c6057763612ed8e35b3f14f756a38a276c7a7612d42cdf582f7061eb634c2d

View on Chainz ↗

Height

#1,477,595

Difficulty

10.705032

Transactions

Size

1.51 KB

Version

Bits

0ab47d02

Nonce

1,322,308,560

Timestamp

2/29/2016, 8:04:43 PM

Confirmations

5,339,081

Mined by

⛏️ P2SHAJt9RihPAspoGYxEFwrD9gXEY9ZbcAhQke

Merkle Root

d0c2593db42201f69fa6904af507f33105faf29dc48e84e2f4d7fd93b3dd1811

Transactions (2)

Coinbase3cad9d5fd24982…10dd90a51539e4

1 in → 1 out8.7300 XPM110 B

AJt9RihP…ZbcAhQke

10ca7c4a4c9a2c…f7e37ba056d8ae

1 in → 35 out212.6072 XPM1.32 KB

APGdziGW…3ou8jPJi AHuRmepb…cdUEymy8 AFzJsByB…cv1Lf5CS ANvZ9LKe…G51LU5Re AeqD6gV4…JU5rkbef

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.

2.841 × 10⁹⁶(97-digit number)

28412871110722142998…28965093460894018559

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

2.841 × 10⁹⁶(97-digit number)

28412871110722142998…28965093460894018559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.841 × 10⁹⁶(97-digit number)

28412871110722142998…28965093460894018561

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

5.682 × 10⁹⁶(97-digit number)

56825742221444285997…57930186921788037119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.682 × 10⁹⁶(97-digit number)

56825742221444285997…57930186921788037121

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

1.136 × 10⁹⁷(98-digit number)

11365148444288857199…15860373843576074239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.136 × 10⁹⁷(98-digit number)

11365148444288857199…15860373843576074241

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

2.273 × 10⁹⁷(98-digit number)

22730296888577714398…31720747687152148479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.273 × 10⁹⁷(98-digit number)

22730296888577714398…31720747687152148481

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

4.546 × 10⁹⁷(98-digit number)

45460593777155428797…63441495374304296959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.546 × 10⁹⁷(98-digit number)

45460593777155428797…63441495374304296961

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 #1,477,595

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