Block #1,433,022

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/28/2016, 3:03:32 PM · Difficulty 10.7925 · 5,400,822 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

732b4de24a7f9434890c14edf5893501e1e1a0bde622aa5011173c477588b94c

View on Chainz ↗

Height

#1,433,022

Difficulty

10.792535

Transactions

Size

903 B

Version

Bits

0acae392

Nonce

512,142,297

Timestamp

1/28/2016, 3:03:32 PM

Confirmations

5,400,822

Mined by

⛏️ P2SHAGio9z8zbNizpMeriDg3Ke9bk2XW5Xy5Hj

Merkle Root

87c9d38f18f6ccf551b25eee741bc506db6ae88cd901c5159f759ac7a943d766

Transactions (2)

Coinbaseeb9e0f966b64d5…445da2bc2e01b9

1 in → 1 out8.5800 XPM110 B

AGio9z8z…XW5Xy5Hj

b4831172d18b06…9129ff71be472a

1 in → 16 out171.0726 XPM703 B

AXbqV9PY…Vo2Ekhd4 AXisyknQ…ZTUGCTrx AH85Tp5C…heWo6AoQ AapdQ3P9…rETW3fTd AW6zRY4z…ELnj21DS

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.

5.275 × 10⁹⁵(96-digit number)

52758785696062531552…72563034418698035199

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

5.275 × 10⁹⁵(96-digit number)

52758785696062531552…72563034418698035199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.275 × 10⁹⁵(96-digit number)

52758785696062531552…72563034418698035201

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

1.055 × 10⁹⁶(97-digit number)

10551757139212506310…45126068837396070399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.055 × 10⁹⁶(97-digit number)

10551757139212506310…45126068837396070401

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

2.110 × 10⁹⁶(97-digit number)

21103514278425012620…90252137674792140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.110 × 10⁹⁶(97-digit number)

21103514278425012620…90252137674792140801

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

4.220 × 10⁹⁶(97-digit number)

42207028556850025241…80504275349584281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.220 × 10⁹⁶(97-digit number)

42207028556850025241…80504275349584281601

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

8.441 × 10⁹⁶(97-digit number)

84414057113700050483…61008550699168563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.441 × 10⁹⁶(97-digit number)

84414057113700050483…61008550699168563201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.688 × 10⁹⁷(98-digit number)

16882811422740010096…22017101398337126399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,433,022

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