Block #2,446,035

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/28/2017, 1:25:09 PM · Difficulty 10.9415 · 4,384,723 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb505e1d2e71d8b67a36a44141f18cb7611a77981285a38c3b7f72e4e7fb2534

View on Chainz ↗

Height

#2,446,035

Difficulty

10.941487

Transactions

Size

6.19 KB

Version

Bits

0af10543

Nonce

1,621,789,449

Timestamp

12/28/2017, 1:25:09 PM

Confirmations

4,384,723

Mined by

⛏️ P2SHAJj5m56ZeeBfoNzqG9gVJDVuAC4rycqM9x

Merkle Root

a1164c91ad09169ad6b6e22a575acb73d26f30326be047d4dcef45d055fb4e95

Transactions (2)

Coinbase51ee527662f4cf…9dcc9359763537

1 in → 1 out8.4300 XPM109 B

AJj5m56Z…4rycqM9x

7b163b61df2fac…ed7196371b7db0

41 in → 2 out702.9310 XPM6.00 KB

AUuGJCHc…Ppzx5mB6 AbqePSBX…riLx7XTx

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.

1.300 × 10⁹⁵(96-digit number)

13009974061460628621…43279045798501240959

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

1.300 × 10⁹⁵(96-digit number)

13009974061460628621…43279045798501240959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.300 × 10⁹⁵(96-digit number)

13009974061460628621…43279045798501240961

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

2.601 × 10⁹⁵(96-digit number)

26019948122921257242…86558091597002481919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.601 × 10⁹⁵(96-digit number)

26019948122921257242…86558091597002481921

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

5.203 × 10⁹⁵(96-digit number)

52039896245842514484…73116183194004963839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.203 × 10⁹⁵(96-digit number)

52039896245842514484…73116183194004963841

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

1.040 × 10⁹⁶(97-digit number)

10407979249168502896…46232366388009927679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.040 × 10⁹⁶(97-digit number)

10407979249168502896…46232366388009927681

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

2.081 × 10⁹⁶(97-digit number)

20815958498337005793…92464732776019855359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.081 × 10⁹⁶(97-digit number)

20815958498337005793…92464732776019855361

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 #2,446,035

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