Block #2,927,118

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/17/2018, 4:14:14 PM · Difficulty 11.3608 · 3,904,431 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

430bc9222842a52219f9bcea7557529b0ed39724e8613c705e8cba2a0e199806

View on Chainz ↗

Height

#2,927,118

Difficulty

11.360807

Transactions

Size

1.06 KB

Version

Bits

0b5c5dd8

Nonce

879,006,679

Timestamp

11/17/2018, 4:14:14 PM

Confirmations

3,904,431

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

cdc7cfead4827f70c0ec5c99f87744d5ab787a77e1b1ebe38710c4e78906f648

Transactions (5)

Coinbase25e9be9f4fa295…2970a12ea728bb

1 in → 1 out7.7800 XPM110 B

AUMQRepm…tAfKmdW1

e7b486c586d424…604655c516c5fb

2 in → 2 out15.4800 XPM305 B

AYiVkR5s…Waom7bcN AbXwmGxD…4XXYP765

7e5245cab99b1c…e2e9f6f1eb13de

1 in → 2 out7.7300 XPM192 B

AbXwmGxD…4XXYP765 AUHBKKGB…mR5KpgvJ

ea93ccfaec8483…4f9436e4984e5e

1 in → 2 out7.7300 XPM193 B

AadFZeqL…sPk6hBJP AbXwmGxD…4XXYP765

75fdfd096d1816…96cad73ab589f4

1 in → 2 out7.7300 XPM192 B

AaKpjPCA…pgnWa4ND AbXwmGxD…4XXYP765

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.

1.689 × 10⁹⁵(96-digit number)

16897812485196092030…40671971972148535679

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

1.689 × 10⁹⁵(96-digit number)

16897812485196092030…40671971972148535679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.689 × 10⁹⁵(96-digit number)

16897812485196092030…40671971972148535681

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

3.379 × 10⁹⁵(96-digit number)

33795624970392184061…81343943944297071359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.379 × 10⁹⁵(96-digit number)

33795624970392184061…81343943944297071361

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

6.759 × 10⁹⁵(96-digit number)

67591249940784368122…62687887888594142719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.759 × 10⁹⁵(96-digit number)

67591249940784368122…62687887888594142721

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

1.351 × 10⁹⁶(97-digit number)

13518249988156873624…25375775777188285439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.351 × 10⁹⁶(97-digit number)

13518249988156873624…25375775777188285441

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

2.703 × 10⁹⁶(97-digit number)

27036499976313747249…50751551554376570879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.703 × 10⁹⁶(97-digit number)

27036499976313747249…50751551554376570881

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.407 × 10⁹⁶(97-digit number)

54072999952627494498…01503103108753141759

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,927,118

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