Block #209,661

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 4:53:24 PM · Difficulty 9.9106 · 6,604,884 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec220977e6ff6e619bb02434fc29ec4756352f42cec3adbf5e65f8ea9f7bc8cd

View on Chainz ↗

Height

#209,661

Difficulty

9.910622

Transactions

Size

5.29 KB

Version

Bits

09e91e87

Nonce

22,991

Timestamp

10/14/2013, 4:53:24 PM

Confirmations

6,604,884

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

19271f63381336ed1b3eb30a0dda890dc2321ea1c236190b7d2abb84a4d43d27

Transactions (2)

Coinbase04a60d70e7dadc…d6fcb2bd029486

1 in → 1 out10.2300 XPM110 B

AbuU1HhS…JPwsJEbB

eddf0a15eeea53…86a777858d0e9d

45 in → 1 out457.8700 XPM5.09 KB

ASePrqts…mAVvmZb9

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.

2.748 × 10⁹⁴(95-digit number)

27484509758557245612…04039096905379134749

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

2.748 × 10⁹⁴(95-digit number)

27484509758557245612…04039096905379134749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.748 × 10⁹⁴(95-digit number)

27484509758557245612…04039096905379134751

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

5.496 × 10⁹⁴(95-digit number)

54969019517114491225…08078193810758269499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.496 × 10⁹⁴(95-digit number)

54969019517114491225…08078193810758269501

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

1.099 × 10⁹⁵(96-digit number)

10993803903422898245…16156387621516538999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.099 × 10⁹⁵(96-digit number)

10993803903422898245…16156387621516539001

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

2.198 × 10⁹⁵(96-digit number)

21987607806845796490…32312775243033077999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.198 × 10⁹⁵(96-digit number)

21987607806845796490…32312775243033078001

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

4.397 × 10⁹⁵(96-digit number)

43975215613691592980…64625550486066155999

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 #209,661

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