Block #2,932,587

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/21/2018, 6:13:21 AM · Difficulty 11.3989 · 3,901,147 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa36404c29ea2fd036c000fe0fb3ac323e1022167e7634e5ec5deb9c069ba54e

View on Chainz ↗

Height

#2,932,587

Difficulty

11.398890

Transactions

Size

1.14 KB

Version

Bits

0b661da8

Nonce

755,318,984

Timestamp

11/21/2018, 6:13:21 AM

Confirmations

3,901,147

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

189fb8df321a57d22ee26332bd4056b0fd1315db3f7df915f999829330918fff

Transactions (2)

Coinbase91cc54c3773a78…f8aa24d35b7ba9

1 in → 1 out7.6900 XPM110 B

AUMQRepm…tAfKmdW1

547709513fd3f2…43dc91d29bc11a

6 in → 2 out13000.0099 XPM963 B

AMpyYZGP…uXpiAVCS AXGggyjc…rv5SbDNP

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.

3.403 × 10⁹⁷(98-digit number)

34032368014054729440…11731713837945323519

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

3.403 × 10⁹⁷(98-digit number)

34032368014054729440…11731713837945323519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.403 × 10⁹⁷(98-digit number)

34032368014054729440…11731713837945323521

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

6.806 × 10⁹⁷(98-digit number)

68064736028109458881…23463427675890647039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.806 × 10⁹⁷(98-digit number)

68064736028109458881…23463427675890647041

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

1.361 × 10⁹⁸(99-digit number)

13612947205621891776…46926855351781294079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.361 × 10⁹⁸(99-digit number)

13612947205621891776…46926855351781294081

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

2.722 × 10⁹⁸(99-digit number)

27225894411243783552…93853710703562588159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.722 × 10⁹⁸(99-digit number)

27225894411243783552…93853710703562588161

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

5.445 × 10⁹⁸(99-digit number)

54451788822487567105…87707421407125176319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.445 × 10⁹⁸(99-digit number)

54451788822487567105…87707421407125176321

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

1.089 × 10⁹⁹(100-digit number)

10890357764497513421…75414842814250352639

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 #2,932,587

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