Block #219,164

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/20/2013, 9:08:47 AM · Difficulty 9.9319 · 6,598,604 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9ae45c6457647f629a4e5058adca1770a88858ec3e2e380628f9fdaf5eab2fd

View on Chainz ↗

Height

#219,164

Difficulty

9.931864

Transactions

Size

1.18 KB

Version

Bits

09ee8ea0

Nonce

18,969

Timestamp

10/20/2013, 9:08:47 AM

Confirmations

6,598,604

Mined by

⛏️ P2SHAX7hoj6jmCPnGBEQf6ME7Q2jfUgy2J6U3R

Merkle Root

6ab19a0263f01eff3f6892a851ded981007a35e8b7737a56330d93eb4f0dab68

Transactions (4)

Coinbase62ac9cefcccd0e…35f6edc10fa8ed

1 in → 1 out10.1500 XPM109 B

AX7hoj6j…gy2J6U3R

21dd26b30bfc12…f13d3e045dfe58

1 in → 4 out10.1400 XPM259 B

Aaczr51X…ihkzsM99 AYqaNvye…yMPuUBC4 ARyHReP1…RCDqPuwD AbuU1HhS…JPwsJEbB

d02c52ca5bd23e…134aede99b34c4

2 in → 2 out11.1857 XPM374 B

ASuoUi24…FwBoFbxd AW7iPR7o…TPM5XWts

2477d568c1af9f…cbb9c25e279004

2 in → 2 out14.4344 XPM374 B

AYhLBW3S…GP8ZcTS9 ALL6BtTJ…cp6j3qpk

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.

1.002 × 10⁹³(94-digit number)

10020418054987319800…69027374154756972319

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

1.002 × 10⁹³(94-digit number)

10020418054987319800…69027374154756972319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.002 × 10⁹³(94-digit number)

10020418054987319800…69027374154756972321

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

2.004 × 10⁹³(94-digit number)

20040836109974639600…38054748309513944639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.004 × 10⁹³(94-digit number)

20040836109974639600…38054748309513944641

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

4.008 × 10⁹³(94-digit number)

40081672219949279201…76109496619027889279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.008 × 10⁹³(94-digit number)

40081672219949279201…76109496619027889281

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

8.016 × 10⁹³(94-digit number)

80163344439898558402…52218993238055778559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.016 × 10⁹³(94-digit number)

80163344439898558402…52218993238055778561

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

1.603 × 10⁹⁴(95-digit number)

16032668887979711680…04437986476111557119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.603 × 10⁹⁴(95-digit number)

16032668887979711680…04437986476111557121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #219,164

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