Block #211,569

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/15/2013, 6:53:56 PM · Difficulty 9.9166 · 6,590,934 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a707a7986fab7b7c58a1855c9a20ae81b2983b00221968b2995296e8d612d900

View on Chainz ↗

Height

#211,569

Difficulty

9.916598

Transactions

Size

881 B

Version

Bits

09eaa62b

Nonce

64,154

Timestamp

10/15/2013, 6:53:56 PM

Confirmations

6,590,934

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

712f82657d9a5feaf545e110b0a22fb1f60bd81cb308bf7886de31c6a5a23632

Transactions (3)

Coinbase3298f0a10c941c…68994d03c3eccc

1 in → 1 out10.1700 XPM110 B

AbuU1HhS…JPwsJEbB

6d1952fd54856a…77baaa7474fbc0

3 in → 2 out300.0100 XPM521 B

AcL4FF4e…xoCWrPuL Af39crpC…YR8K5Xm3

37ecc07dd35fe4…24b14ceaca5a96

1 in → 1 out10.2300 XPM159 B

ATV4M1CV…dd9zw8nH

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.

4.879 × 10⁹⁷(98-digit number)

48794878818827227562…84631599525779046399

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

4.879 × 10⁹⁷(98-digit number)

48794878818827227562…84631599525779046399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.879 × 10⁹⁷(98-digit number)

48794878818827227562…84631599525779046401

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

9.758 × 10⁹⁷(98-digit number)

97589757637654455125…69263199051558092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.758 × 10⁹⁷(98-digit number)

97589757637654455125…69263199051558092801

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

1.951 × 10⁹⁸(99-digit number)

19517951527530891025…38526398103116185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.951 × 10⁹⁸(99-digit number)

19517951527530891025…38526398103116185601

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

3.903 × 10⁹⁸(99-digit number)

39035903055061782050…77052796206232371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.903 × 10⁹⁸(99-digit number)

39035903055061782050…77052796206232371201

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

7.807 × 10⁹⁸(99-digit number)

78071806110123564100…54105592412464742399

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