Block #2,242,790

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/8/2017, 5:54:57 PM · Difficulty 10.9474 · 4,583,935 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3018d69ea8395959eb92cf0b71ee1b0dd22f46d3f10c9d5007d4c31d52177e4

View on Chainz ↗

Height

#2,242,790

Difficulty

10.947381

Transactions

Size

1.79 KB

Version

Bits

0af28792

Nonce

1,251,309,929

Timestamp

8/8/2017, 5:54:57 PM

Confirmations

4,583,935

Mined by

⛏️ P2SHAezXRbCtvqmD5EsDGekX9PMEKbYuB4bY6L

Merkle Root

e18aa06990ac1fd032ec2174c1ce66bddba50cb3ac5a5c2f1fd333aa77fc0e35

Transactions (3)

Coinbase8244cc4db309b8…4577936ea6c823

1 in → 1 out8.3600 XPM110 B

AezXRbCt…YuB4bY6L

eb353e23e23e96…425b6f13abdbdd

1 in → 2 out4.3100 XPM226 B

AXZMRcXr…z2dUbCSR APvD3UAe…SASLRWeE

28ad4f0ea01639…30691b7d18be78

9 in → 2 out4.1500 XPM1.38 KB

AWXmZLkQ…UU5EJXx2 AVNP8F4x…o1fu6xcH

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.

7.977 × 10⁹³(94-digit number)

79772298394493508807…98922753389988571599

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

7.977 × 10⁹³(94-digit number)

79772298394493508807…98922753389988571599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.977 × 10⁹³(94-digit number)

79772298394493508807…98922753389988571601

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

1.595 × 10⁹⁴(95-digit number)

15954459678898701761…97845506779977143199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.595 × 10⁹⁴(95-digit number)

15954459678898701761…97845506779977143201

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

3.190 × 10⁹⁴(95-digit number)

31908919357797403523…95691013559954286399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.190 × 10⁹⁴(95-digit number)

31908919357797403523…95691013559954286401

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

6.381 × 10⁹⁴(95-digit number)

63817838715594807046…91382027119908572799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.381 × 10⁹⁴(95-digit number)

63817838715594807046…91382027119908572801

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

1.276 × 10⁹⁵(96-digit number)

12763567743118961409…82764054239817145599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.276 × 10⁹⁵(96-digit number)

12763567743118961409…82764054239817145601

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 #2,242,790

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