Block #215,039

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/17/2013, 8:15:37 PM · Difficulty 9.9249 · 6,599,429 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

246080eb92d21d1c59b2830f56a868ae9f062e92986d4cde9fc513e3c9e3b47b

View on Chainz ↗

Height

#215,039

Difficulty

9.924908

Transactions

Size

803 B

Version

Bits

09ecc6c2

Nonce

68,608

Timestamp

10/17/2013, 8:15:37 PM

Confirmations

6,599,429

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

7feff48f13bec99f01ee37ff85b58eb437139c38fb7b27a74757727cee389655

Transactions (3)

Coinbase8bedba7e80b15d…c8aaf49628587f

1 in → 1 out10.1600 XPM110 B

AbuU1HhS…JPwsJEbB

6945cfde841d17…0dc936171591b0

1 in → 2 out73.8446 XPM226 B

AaZxZr7M…g3GFCpLU AdnAJn2e…2NLN5TCz

300e80a076ef8e…2a44a0f7fe4688

2 in → 2 out12.1829 XPM376 B

AUx7Gd2a…8PwgXmUB ASuoUi24…FwBoFbxd

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.

1.423 × 10⁹⁷(98-digit number)

14230246148893549064…67872696729803386879

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

1.423 × 10⁹⁷(98-digit number)

14230246148893549064…67872696729803386879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.423 × 10⁹⁷(98-digit number)

14230246148893549064…67872696729803386881

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

2.846 × 10⁹⁷(98-digit number)

28460492297787098129…35745393459606773759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.846 × 10⁹⁷(98-digit number)

28460492297787098129…35745393459606773761

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

5.692 × 10⁹⁷(98-digit number)

56920984595574196258…71490786919213547519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.692 × 10⁹⁷(98-digit number)

56920984595574196258…71490786919213547521

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

1.138 × 10⁹⁸(99-digit number)

11384196919114839251…42981573838427095039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.138 × 10⁹⁸(99-digit number)

11384196919114839251…42981573838427095041

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

2.276 × 10⁹⁸(99-digit number)

22768393838229678503…85963147676854190079

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 #215,039

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