Block #466,119

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 11:05:15 PM · Difficulty 10.4218 · 6,351,236 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0f91a3f9863fc4d52bc0e9aea3b228b7cdc377f9e243d62f70eaf2749a29457

View on Chainz ↗

Height

#466,119

Difficulty

10.421755

Transactions

Size

1.66 KB

Version

Bits

0a6bf823

Nonce

2,870

Timestamp

3/29/2014, 11:05:15 PM

Confirmations

6,351,236

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0ca309f9a3d3b133c412c4f61ae62ecc686bc408dc6d5a0910f30dbe126026dc

Transactions (5)

Coinbase824e9af5a91e92…7adc834ceda67b

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

74281826f0c073…bae99a9751721c

2 in → 2 out11.6989 XPM374 B

AM9gxnSA…EBSVq4PJ ARQpRQhn…kwV9Qyfp

940729d418ec6a…ac9ebbe0373d98

4 in → 2 out4.9032 XPM668 B

AZjnkR14…zKjC9Ezw AbD4otEU…jFd32mLZ

aac2f25d411013…de19ac4441c32a

1 in → 2 out7.1655 XPM225 B

Acjz69Qu…ddRoASqd ALPV199F…QuvZZ3xm

f5c0368357b76b…9f443e6df59dd3

1 in → 2 out7.1616 XPM226 B

AQeUi7XU…CDZwc7uB AH4Qg8vE…gDHuV1dB

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.

3.064 × 10⁹⁸(99-digit number)

30645238092247245349…66628656268537425919

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

3.064 × 10⁹⁸(99-digit number)

30645238092247245349…66628656268537425919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.064 × 10⁹⁸(99-digit number)

30645238092247245349…66628656268537425921

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

6.129 × 10⁹⁸(99-digit number)

61290476184494490699…33257312537074851839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.129 × 10⁹⁸(99-digit number)

61290476184494490699…33257312537074851841

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

1.225 × 10⁹⁹(100-digit number)

12258095236898898139…66514625074149703679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.225 × 10⁹⁹(100-digit number)

12258095236898898139…66514625074149703681

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

2.451 × 10⁹⁹(100-digit number)

24516190473797796279…33029250148299407359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.451 × 10⁹⁹(100-digit number)

24516190473797796279…33029250148299407361

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

4.903 × 10⁹⁹(100-digit number)

49032380947595592559…66058500296598814719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.903 × 10⁹⁹(100-digit number)

49032380947595592559…66058500296598814721

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 #466,119

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