Block #220,114

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 8:36:42 PM · Difficulty 9.9346 · 6,589,774 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f4956f3a41825fdf89698599c05728316860821b5b688dc045b1601a7d22bc03

View on Chainz ↗

Height

#220,114

Difficulty

9.934578

Transactions

Size

877 B

Version

Bits

09ef4089

Nonce

199,754

Timestamp

10/20/2013, 8:36:42 PM

Confirmations

6,589,774

Mined by

⛏️ P2SHAG48788rCNhydD8wkMVRp16CAH2cGoQfhR

Merkle Root

9a738ce37138fb368a307b398807ebaaefcebb138567655f20075c2eea5dd130

Transactions (4)

Coinbase525775f8b424d9…8c37d500a6f133

1 in → 1 out10.1500 XPM109 B

AG48788r…2cGoQfhR

c5200de5d6d03f…32a2282e6956c6

1 in → 2 out10.1200 XPM227 B

AQDaBKCb…kujkc9p4 Abx5qH6G…Hh56BvNt

cb851cbeba6683…aa8c0825184e62

1 in → 2 out10.1200 XPM226 B

AWSsuN81…j2tnb4Ru AaHaNnZZ…w5CtpS4F

b094eb6c6882a8…2fe46f606557c2

1 in → 2 out3.3256 XPM225 B

Af2AbxLH…7CxCYNAm ASyL3JZF…2Mf9V5tj

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.

1.956 × 10⁹⁵(96-digit number)

19569082428194063696…11063976822540037119

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

1.956 × 10⁹⁵(96-digit number)

19569082428194063696…11063976822540037119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.956 × 10⁹⁵(96-digit number)

19569082428194063696…11063976822540037121

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

3.913 × 10⁹⁵(96-digit number)

39138164856388127392…22127953645080074239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.913 × 10⁹⁵(96-digit number)

39138164856388127392…22127953645080074241

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

7.827 × 10⁹⁵(96-digit number)

78276329712776254784…44255907290160148479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.827 × 10⁹⁵(96-digit number)

78276329712776254784…44255907290160148481

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

1.565 × 10⁹⁶(97-digit number)

15655265942555250956…88511814580320296959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.565 × 10⁹⁶(97-digit number)

15655265942555250956…88511814580320296961

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

3.131 × 10⁹⁶(97-digit number)

31310531885110501913…77023629160640593919

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 #220,114

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