Block #420,024

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/26/2014, 3:09:12 AM · Difficulty 10.3651 · 6,421,640 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5e8bd705f07cc98a3520a088b3f7154468e1835d6ae9759ce2c2f91645ae707

View on Chainz ↗

Height

#420,024

Difficulty

10.365068

Transactions

Size

871 B

Version

Bits

0a5d7512

Nonce

425,654

Timestamp

2/26/2014, 3:09:12 AM

Confirmations

6,421,640

Mined by

⛏️ h?-AcuM7XiJ6QSTDXS73zz3uhVx2G5uND8Jce

Merkle Root

12b14b4d2edf4e2857ca1626d5c6a331a1823596a099364705848f7da35a68b2

Transactions (1)

Coinbase12b14b4d2edf4e…848f7da35a68b2

1 in → 21 out9.2900 XPM777 B

AcuM7XiJ…5uND8Jce AVRMvm7T…6PC6keBx AdFLJFhb…bsaVkAyh AZqjMFvv…G8aw2zC8 AZuKpVkB…HFoeLG6t

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.

1.183 × 10¹⁰⁵(106-digit number)

11833081870931881382…57356297709865587199

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

1.183 × 10¹⁰⁵(106-digit number)

11833081870931881382…57356297709865587199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.183 × 10¹⁰⁵(106-digit number)

11833081870931881382…57356297709865587201

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

2.366 × 10¹⁰⁵(106-digit number)

23666163741863762764…14712595419731174399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.366 × 10¹⁰⁵(106-digit number)

23666163741863762764…14712595419731174401

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

4.733 × 10¹⁰⁵(106-digit number)

47332327483727525529…29425190839462348799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.733 × 10¹⁰⁵(106-digit number)

47332327483727525529…29425190839462348801

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

9.466 × 10¹⁰⁵(106-digit number)

94664654967455051059…58850381678924697599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.466 × 10¹⁰⁵(106-digit number)

94664654967455051059…58850381678924697601

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

1.893 × 10¹⁰⁶(107-digit number)

18932930993491010211…17700763357849395199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.893 × 10¹⁰⁶(107-digit number)

18932930993491010211…17700763357849395201

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

3.786 × 10¹⁰⁶(107-digit number)

37865861986982020423…35401526715698790399

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 #420,024

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