Block #2,643,481

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/2/2018, 3:07:19 AM · Difficulty 11.6846 · 4,187,148 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40466555eddbf1ab2429af14f69b12deec0d4cf6eb0e8a03bf020f33b9eeb06b

View on Chainz ↗

Height

#2,643,481

Difficulty

11.684631

Transactions

Size

1.08 KB

Version

Bits

0baf43f8

Nonce

458,813,905

Timestamp

5/2/2018, 3:07:19 AM

Confirmations

4,187,148

Mined by

⛏️ P2SHAK1FQz9FGjQbGd6irNpsj6FyyHduCxbMC8

Merkle Root

67e12affaadb3c74617729a45db2ddeac5b9480a99294b77f7be8652a1d1c817

Transactions (5)

Coinbase76d395dcf11f11…0d4f4ff334df9e

1 in → 1 out7.3500 XPM110 B

AK1FQz9F…duCxbMC8

2caca3b42392f0…d9a6251fb5af8b

1 in → 2 out4.3453 XPM225 B

Ab5u6pek…qT8gfi7D AXU2VgsN…RePZXTgf

59da174977e767…6573c815d6794f

1 in → 2 out2.2609 XPM225 B

APkZ9k1o…jaVW5bLR ATt8vVZX…8WgwsJUS

00c752e9881872…f14533e02b8dd4

1 in → 2 out1.3464 XPM225 B

AdHbmA57…EfcBnuqg AYrVVyHX…izr1k7kM

37777ca39ee478…a1c9a023584819

1 in → 2 out1.6295 XPM227 B

AS8rLEGE…wBT1FkGK AUMzbGAY…jZC41bzQ

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.

6.886 × 10⁹²(93-digit number)

68869682848876814462…34520402666916721539

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

6.886 × 10⁹²(93-digit number)

68869682848876814462…34520402666916721539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.886 × 10⁹²(93-digit number)

68869682848876814462…34520402666916721541

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

1.377 × 10⁹³(94-digit number)

13773936569775362892…69040805333833443079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.377 × 10⁹³(94-digit number)

13773936569775362892…69040805333833443081

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

2.754 × 10⁹³(94-digit number)

27547873139550725785…38081610667666886159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.754 × 10⁹³(94-digit number)

27547873139550725785…38081610667666886161

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

5.509 × 10⁹³(94-digit number)

55095746279101451570…76163221335333772319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.509 × 10⁹³(94-digit number)

55095746279101451570…76163221335333772321

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

1.101 × 10⁹⁴(95-digit number)

11019149255820290314…52326442670667544639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.101 × 10⁹⁴(95-digit number)

11019149255820290314…52326442670667544641

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

2.203 × 10⁹⁴(95-digit number)

22038298511640580628…04652885341335089279

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

2.203 × 10⁹⁴(95-digit number)

22038298511640580628…04652885341335089281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,643,481

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