Block #2,129,976

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2017, 2:57:13 AM · Difficulty 10.9095 · 4,687,174 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94f59f1d506eb739b85df670705bd33fa5e174cdfbb34ff08da9f441028c9f5c

View on Chainz ↗

Height

#2,129,976

Difficulty

10.909451

Transactions

Size

1.87 KB

Version

Bits

0ae8d1cf

Nonce

453,804,564

Timestamp

5/24/2017, 2:57:13 AM

Confirmations

4,687,174

Mined by

⛏️ P2SHAHcMXmyA8T7vZNyLw2kVckStFyBaBxZLCS

Merkle Root

eaa2cf355365c059692b38257382e6ce22c7ed4139837a964a9f213da7fa7107

Transactions (3)

Coinbasef154e461f96afa…5b9d3890c14599

1 in → 1 out8.4400 XPM110 B

AHcMXmyA…BaBxZLCS

1b9eb7445d31f3…2fab675eb11b9d

10 in → 1 out2416.5027 XPM1.49 KB

ANr6WH7B…owEdSWEE

e49ffce096735f…ae3c22907d6d05

1 in → 1 out15.9900 XPM192 B

ANr6WH7B…owEdSWEE

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.

1.282 × 10⁹⁵(96-digit number)

12820809623859900441…99552956223691189759

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

1.282 × 10⁹⁵(96-digit number)

12820809623859900441…99552956223691189759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.282 × 10⁹⁵(96-digit number)

12820809623859900441…99552956223691189761

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

2.564 × 10⁹⁵(96-digit number)

25641619247719800882…99105912447382379519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.564 × 10⁹⁵(96-digit number)

25641619247719800882…99105912447382379521

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

5.128 × 10⁹⁵(96-digit number)

51283238495439601765…98211824894764759039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.128 × 10⁹⁵(96-digit number)

51283238495439601765…98211824894764759041

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

1.025 × 10⁹⁶(97-digit number)

10256647699087920353…96423649789529518079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.025 × 10⁹⁶(97-digit number)

10256647699087920353…96423649789529518081

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

2.051 × 10⁹⁶(97-digit number)

20513295398175840706…92847299579059036159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.051 × 10⁹⁶(97-digit number)

20513295398175840706…92847299579059036161

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 #2,129,976

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