Block #3,476,194

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/15/2019, 12:40:19 AM · Difficulty 10.9791 · 3,351,173 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

840bf75eab16582f81cfea7b345a7c5a52efc2cb98eb2ce18ef08b3870cba0ba

View on Chainz ↗

Height

#3,476,194

Difficulty

10.979076

Transactions

Size

508 B

Version

Bits

0afaa4c0

Nonce

65,035,523

Timestamp

12/15/2019, 12:40:19 AM

Confirmations

3,351,173

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

1523d47b73eecdc2ffb2e2f0c80081d1403f213474538d52936891e7b77c4086

Transactions (2)

Coinbased7a43655b890b7…d57d9bbc270a11

1 in → 1 out8.2900 XPM110 B

ASiq2qtK…VMhmk7yL

f88872487c0c1c…e430a22363725a

2 in → 2 out16.5800 XPM307 B

AaTLXdNM…Jn8m3nLr AeHXpz5Q…WLPHByEV

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.

9.896 × 10⁹⁶(97-digit number)

98961748859852917886…14576536441072441599

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

9.896 × 10⁹⁶(97-digit number)

98961748859852917886…14576536441072441599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.896 × 10⁹⁶(97-digit number)

98961748859852917886…14576536441072441601

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

1.979 × 10⁹⁷(98-digit number)

19792349771970583577…29153072882144883199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.979 × 10⁹⁷(98-digit number)

19792349771970583577…29153072882144883201

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

3.958 × 10⁹⁷(98-digit number)

39584699543941167154…58306145764289766399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.958 × 10⁹⁷(98-digit number)

39584699543941167154…58306145764289766401

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

7.916 × 10⁹⁷(98-digit number)

79169399087882334309…16612291528579532799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.916 × 10⁹⁷(98-digit number)

79169399087882334309…16612291528579532801

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

1.583 × 10⁹⁸(99-digit number)

15833879817576466861…33224583057159065599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.583 × 10⁹⁸(99-digit number)

15833879817576466861…33224583057159065601

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

3.166 × 10⁹⁸(99-digit number)

31667759635152933723…66449166114318131199

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 #3,476,194

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