Block #2,063,027

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2017, 5:33:37 AM · Difficulty 10.8544 · 4,777,311 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

861e02ba8fabcca65eeed78ab864cafd8bec223c92b54ceced80748c0f2f4892

View on Chainz ↗

Height

#2,063,027

Difficulty

10.854351

Transactions

Size

1.18 KB

Version

Bits

0adab6be

Nonce

1,552,675,713

Timestamp

4/9/2017, 5:33:37 AM

Confirmations

4,777,311

Mined by

⛏️ P2SHAVSTZ4Wq1d1RRBfmZYtw8pap8PRYfzkdgc

Merkle Root

02bbd1ed1c06086c427797875bbfa16c96ec28a910521278ace0a09877b4f36b

Transactions (3)

Coinbasee07958833546fc…7039b759c8ebbf

1 in → 1 out8.4900 XPM109 B

AVSTZ4Wq…RYfzkdgc

05483f30c540d9…9cbafff26d29a6

1 in → 1 out9999.9900 XPM192 B

AKc8GdcV…PFmVnxov

2be813528806d6…9f89ca98d330f3

5 in → 2 out257.2366 XPM817 B

AYoy228q…feZqXfNq Af4kg6ov…NZZCcMDG

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.

1.133 × 10⁹⁵(96-digit number)

11337511011401614972…25236697019965048959

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

1.133 × 10⁹⁵(96-digit number)

11337511011401614972…25236697019965048959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.133 × 10⁹⁵(96-digit number)

11337511011401614972…25236697019965048961

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

2.267 × 10⁹⁵(96-digit number)

22675022022803229944…50473394039930097919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.267 × 10⁹⁵(96-digit number)

22675022022803229944…50473394039930097921

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

4.535 × 10⁹⁵(96-digit number)

45350044045606459889…00946788079860195839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.535 × 10⁹⁵(96-digit number)

45350044045606459889…00946788079860195841

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

9.070 × 10⁹⁵(96-digit number)

90700088091212919779…01893576159720391679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.070 × 10⁹⁵(96-digit number)

90700088091212919779…01893576159720391681

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

1.814 × 10⁹⁶(97-digit number)

18140017618242583955…03787152319440783359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.814 × 10⁹⁶(97-digit number)

18140017618242583955…03787152319440783361

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 #2,063,027

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