Block #221,852

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 7:43:41 PM · Difficulty 9.9398 · 6,587,082 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b35683bd636a2e3010f43a73f2b6acc3198e23fd1ff971bc94ab785e1b7e93e9

View on Chainz ↗

Height

#221,852

Difficulty

9.939764

Transactions

Size

1.11 KB

Version

Bits

09f09460

Nonce

15,138

Timestamp

10/21/2013, 7:43:41 PM

Confirmations

6,587,082

Mined by

⛏️ P2SHAKqUhbEYmeVyq7wENmBL5LD2LdBVPJQLWn

Merkle Root

cd38b403f5ffda658e357a3bb0b2175cdaecb8522c5467d151260c00196c321b

Transactions (5)

Coinbase5660331d64b4e0…e6fd20c8b18347

1 in → 1 out10.1500 XPM109 B

AKqUhbEY…BVPJQLWn

3eb0180010efd8…1ae1f5a5c64395

1 in → 2 out10.1100 XPM225 B

AYeXybnc…Lk1tyUhW AGAf8Z9Q…ggDWo52w

e5aa2b012a4dde…b9456009199db6

1 in → 2 out10.1100 XPM226 B

ATGfMkYo…fQf7KBRy AUfBNY3y…Mm2UYiNj

615abfd05156b0…2ce9ae21448929

1 in → 4 out10.1100 XPM260 B

AMcKV4FC…1xqRV8Qf Acs9SHrk…QJSB8SFG AbuU1HhS…JPwsJEbB AdToHhys…uNu3dqWo

9e64facd37b3f5…3a6df2625718f4

1 in → 2 out8.0984 XPM225 B

ARC34c2B…XiBBrx4X AKopCYGU…oD4tyS1y

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.

5.055 × 10⁹⁹(100-digit number)

50553384673710386627…12348425797936928639

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

5.055 × 10⁹⁹(100-digit number)

50553384673710386627…12348425797936928639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.055 × 10⁹⁹(100-digit number)

50553384673710386627…12348425797936928641

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

1.011 × 10¹⁰⁰(101-digit number)

10110676934742077325…24696851595873857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.011 × 10¹⁰⁰(101-digit number)

10110676934742077325…24696851595873857281

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

2.022 × 10¹⁰⁰(101-digit number)

20221353869484154651…49393703191747714559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.022 × 10¹⁰⁰(101-digit number)

20221353869484154651…49393703191747714561

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

4.044 × 10¹⁰⁰(101-digit number)

40442707738968309302…98787406383495429119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.044 × 10¹⁰⁰(101-digit number)

40442707738968309302…98787406383495429121

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

8.088 × 10¹⁰⁰(101-digit number)

80885415477936618604…97574812766990858239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #221,852

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