Block #244,224

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 5:50:36 PM · Difficulty 9.9627 · 6,550,069 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00be01f6db058bed7e29918255a9df7ce38120312412049b3e6160cfa5d2256e

View on Chainz ↗

Height

#244,224

Difficulty

9.962696

Transactions

Size

1.22 KB

Version

Bits

09f67347

Nonce

252

Timestamp

11/4/2013, 5:50:36 PM

Confirmations

6,550,069

Merkle Root

7b81a6edc50efee5016c1aed83373a418f38a2307c5318ee684a8ba1017332bd

Transactions (5)

Coinbase01bc6819aba5c0…60e253f24351c4

1 in → 2 out10.1051 XPM137 B

AZDUEbdS…RYKMRZET Abiw8n3q…ZnZfgvQW

8a570947ba5f9a…084d94ae33ac84

2 in → 2 out23.2041 XPM375 B

AJu3LNhi…tMmARoYS AN7UXj1g…Ro4yTmrC

21b8af3d7bcc42…b027bd5a8825be

1 in → 1 out1.9900 XPM192 B

AZhoN24d…Ck33eQcc

628c2aaacdc65f…e028e0a4701d92

1 in → 2 out6.0182 XPM226 B

Abovapjo…q1CCaXPD AHktqdSR…Dczo5JBs

688470477c1e03…124ac62d40cea2

1 in → 2 out2.9956 XPM226 B

AbTwcWdR…RSy1qa5R AZqxGVA4…66YSAqQg

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.

1.318 × 10⁹⁹(100-digit number)

13181354709267482940…00423074030879111999

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

1.318 × 10⁹⁹(100-digit number)

13181354709267482940…00423074030879111999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.318 × 10⁹⁹(100-digit number)

13181354709267482940…00423074030879112001

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

2.636 × 10⁹⁹(100-digit number)

26362709418534965881…00846148061758223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.636 × 10⁹⁹(100-digit number)

26362709418534965881…00846148061758224001

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

5.272 × 10⁹⁹(100-digit number)

52725418837069931762…01692296123516447999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.272 × 10⁹⁹(100-digit number)

52725418837069931762…01692296123516448001

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

1.054 × 10¹⁰⁰(101-digit number)

10545083767413986352…03384592247032895999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.054 × 10¹⁰⁰(101-digit number)

10545083767413986352…03384592247032896001

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

2.109 × 10¹⁰⁰(101-digit number)

21090167534827972704…06769184494065791999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.109 × 10¹⁰⁰(101-digit number)

21090167534827972704…06769184494065792001

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