Block #2,051,919

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2017, 4:36:25 PM · Difficulty 10.7278 · 4,774,920 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

832abea8e5d04efbb9c824c7097d180ea13f573970e22b7f95142a9231c82b84

View on Chainz ↗

Height

#2,051,919

Difficulty

10.727843

Transactions

Size

652 B

Version

Bits

0aba53ed

Nonce

23,674,704

Timestamp

4/3/2017, 4:36:25 PM

Confirmations

4,774,920

Mined by

⛏️ P2SHAUY8iHzD5Qm9NG3Qmk35eXUf4zBygDY6J1

Merkle Root

2807c3916189277da6f7135a35a705e9867149cc67c0c63732424e0f3475c872

Transactions (3)

Coinbase239c340202c236…d4412fc707b25a

1 in → 1 out8.7000 XPM109 B

AUY8iHzD…BygDY6J1

4a9ba4c9a9fd53…2c4e4012969f73

1 in → 2 out9999.9900 XPM227 B

ATHYgn6C…HXHkeD2m AVa5dYbR…j5uZYCvt

9eef00d9ebb6e9…857123a7d334b7

1 in → 2 out1773.0081 XPM226 B

AR1eaXi7…iVTtCTVy AY5aCFdt…7mcvwiGJ

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.

1.331 × 10⁹⁵(96-digit number)

13317032901561494783…02523702033115029759

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

1.331 × 10⁹⁵(96-digit number)

13317032901561494783…02523702033115029759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.331 × 10⁹⁵(96-digit number)

13317032901561494783…02523702033115029761

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

2.663 × 10⁹⁵(96-digit number)

26634065803122989566…05047404066230059519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.663 × 10⁹⁵(96-digit number)

26634065803122989566…05047404066230059521

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

5.326 × 10⁹⁵(96-digit number)

53268131606245979133…10094808132460119039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.326 × 10⁹⁵(96-digit number)

53268131606245979133…10094808132460119041

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

1.065 × 10⁹⁶(97-digit number)

10653626321249195826…20189616264920238079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.065 × 10⁹⁶(97-digit number)

10653626321249195826…20189616264920238081

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

2.130 × 10⁹⁶(97-digit number)

21307252642498391653…40379232529840476159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.130 × 10⁹⁶(97-digit number)

21307252642498391653…40379232529840476161

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 #2,051,919

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