Block #2,051,597

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2017, 1:52:27 PM · Difficulty 10.7191 · 4,765,304 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d349a6c33247ef00241a2240705f608f02e9e40ed42e68732ad8f75cce3f1a99

View on Chainz ↗

Height

#2,051,597

Difficulty

10.719134

Transactions

Size

2.00 KB

Version

Bits

0ab81923

Nonce

1,015,904,376

Timestamp

4/3/2017, 1:52:27 PM

Confirmations

4,765,304

Mined by

⛏️ P2SHAVCoZ9aGUtwoJ5CuncA59YRuyvPcbFBibM

Merkle Root

437bb96c936f5851c976ea4c039877e66b485738518231549d725a0e57b71147

Transactions (5)

Coinbase442b27c11bcf06…87fd42756877fc

1 in → 1 out8.7400 XPM110 B

AVCoZ9aG…PcbFBibM

01c75e27bb8c48…e2e871ce34b01f

2 in → 2 out17.4700 XPM306 B

AKVSE3co…BT4a2S8h AbaEAT5m…LNNjUCwh

47e6c840835516…4dae0b2b991e88

1 in → 2 out8.7300 XPM193 B

ALAwHsMj…nMaFubfj AWZFryv3…1z25ZhmM

342054367a6ee5…9319d6e493f457

2 in → 2 out15.6800 XPM339 B

AKDHX5A5…mc1GDnW5 AdwZ4WVB…go21xax8

e411bfcb7e41e3…97b887ab433041

7 in → 1 out20.0000 XPM1011 B

ALjjf6b2…vS4Xe84m

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.

2.285 × 10⁹⁵(96-digit number)

22857971669974676403…22654063489117637759

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

2.285 × 10⁹⁵(96-digit number)

22857971669974676403…22654063489117637759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.285 × 10⁹⁵(96-digit number)

22857971669974676403…22654063489117637761

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

4.571 × 10⁹⁵(96-digit number)

45715943339949352806…45308126978235275519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.571 × 10⁹⁵(96-digit number)

45715943339949352806…45308126978235275521

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

9.143 × 10⁹⁵(96-digit number)

91431886679898705613…90616253956470551039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.143 × 10⁹⁵(96-digit number)

91431886679898705613…90616253956470551041

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

1.828 × 10⁹⁶(97-digit number)

18286377335979741122…81232507912941102079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.828 × 10⁹⁶(97-digit number)

18286377335979741122…81232507912941102081

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

3.657 × 10⁹⁶(97-digit number)

36572754671959482245…62465015825882204159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.657 × 10⁹⁶(97-digit number)

36572754671959482245…62465015825882204161

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 #2,051,597

Cookie Preferences