Block #2,951,430

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/4/2018, 8:33:27 AM · Difficulty 11.3976 · 3,890,752 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a84909e2e296e7241983c81d4e3fca217ffff0712086324da2ab0a38d68703fa

View on Chainz ↗

Height

#2,951,430

Difficulty

11.397570

Transactions

Size

573 B

Version

Bits

0b65c72e

Nonce

33,211,154

Timestamp

12/4/2018, 8:33:27 AM

Confirmations

3,890,752

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

6636c76783c1fe8ccb66438e487799b49698f01c0c4065522698031adcac3dd0

Transactions (2)

Coinbase0cf2ed409213d4…a9af4e6c7f519b

1 in → 1 out7.7000 XPM109 B

AbXwmGxD…4XXYP765

097dc916e7958b…6f78984f1c8764

2 in → 2 out10.0169 XPM374 B

AGcroUje…g5NZNB3Y APpUz1WN…tAMZHabB

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.

4.648 × 10⁹⁵(96-digit number)

46489301566603719104…76795019856626817919

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

4.648 × 10⁹⁵(96-digit number)

46489301566603719104…76795019856626817919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.648 × 10⁹⁵(96-digit number)

46489301566603719104…76795019856626817921

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

9.297 × 10⁹⁵(96-digit number)

92978603133207438208…53590039713253635839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.297 × 10⁹⁵(96-digit number)

92978603133207438208…53590039713253635841

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

1.859 × 10⁹⁶(97-digit number)

18595720626641487641…07180079426507271679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.859 × 10⁹⁶(97-digit number)

18595720626641487641…07180079426507271681

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

3.719 × 10⁹⁶(97-digit number)

37191441253282975283…14360158853014543359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.719 × 10⁹⁶(97-digit number)

37191441253282975283…14360158853014543361

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

7.438 × 10⁹⁶(97-digit number)

74382882506565950566…28720317706029086719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.438 × 10⁹⁶(97-digit number)

74382882506565950566…28720317706029086721

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

1.487 × 10⁹⁷(98-digit number)

14876576501313190113…57440635412058173439

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 #2,951,430

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