Block #369,136

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 5:00:45 AM · Difficulty 10.4444 · 6,439,870 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d280c7492881d7d431b958cc0fdf757055c17bb42be38d645aa700ccb22a808

View on Chainz ↗

Height

#369,136

Difficulty

10.444432

Transactions

Size

1.67 KB

Version

Bits

0a71c64c

Nonce

82,427

Timestamp

1/21/2014, 5:00:45 AM

Confirmations

6,439,870

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7ae0c36fcc0caea5407772d753231bdd01cc0c9b3e554f4ea3feec85f316654a

Transactions (5)

Coinbase29e31a4e37b6cf…e07028e07ee4b4

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

a7e2228a6c8ab8…cc811ccc7f04ec

1 in → 2 out8.1685 XPM227 B

Ab3J4ipo…GaHrWuuW ATQ9wmBr…rXyxUeb1

407a4ac4f642d2…f76ac0d45802f7

1 in → 2 out7.4432 XPM226 B

AQM8vD51…ZifHnd3e AXnL68UR…jsxeGUhN

d18c256f984840…533d4b6db02c28

1 in → 2 out7.1059 XPM225 B

AMo9fCSs…JYAb5Mix AYaHrqRh…REu5vtb4

5d872625e16389…386103d508fa68

5 in → 2 out3.0704 XPM820 B

ASDeCmyn…GNCdmkSh AKxXt2sk…ZZmgfgbD

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.

1.568 × 10¹⁰³(104-digit number)

15685905090148514185…99584088523591054919

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

1.568 × 10¹⁰³(104-digit number)

15685905090148514185…99584088523591054919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.568 × 10¹⁰³(104-digit number)

15685905090148514185…99584088523591054921

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

3.137 × 10¹⁰³(104-digit number)

31371810180297028370…99168177047182109839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.137 × 10¹⁰³(104-digit number)

31371810180297028370…99168177047182109841

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

6.274 × 10¹⁰³(104-digit number)

62743620360594056740…98336354094364219679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.274 × 10¹⁰³(104-digit number)

62743620360594056740…98336354094364219681

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

1.254 × 10¹⁰⁴(105-digit number)

12548724072118811348…96672708188728439359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.254 × 10¹⁰⁴(105-digit number)

12548724072118811348…96672708188728439361

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

2.509 × 10¹⁰⁴(105-digit number)

25097448144237622696…93345416377456878719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.509 × 10¹⁰⁴(105-digit number)

25097448144237622696…93345416377456878721

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 #369,136

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