Block #2,642,024

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/1/2018, 2:00:24 PM · Difficulty 11.6398 · 4,191,281 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eba9817281c4e93b2597f3d6354b729806a94abbf0d040d8ab13843cb04762b7

View on Chainz ↗

Height

#2,642,024

Difficulty

11.639777

Transactions

Size

1.22 KB

Version

Bits

0ba3c86e

Nonce

1,226,903,172

Timestamp

5/1/2018, 2:00:24 PM

Confirmations

4,191,281

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

d6cec06e5b6471c659967d19f266727aede2a026a06797d911ec053a573019c5

Transactions (3)

Coinbaseb964c41213cb87…2823c11e454f67

1 in → 1 out7.3900 XPM110 B

Adqah8zh…1WwoHJ9t

d416d991e6c406…de8a40d365f38d

1 in → 2 out292975.8435 XPM226 B

AUNdQbQX…nbPFgr1Z AKjgrGPV…n8jeijkL

8b3180058a5727…e5ddbfd74aaadb

5 in → 2 out59.9900 XPM820 B

AQWr7kPD…s9DUaAU5 AKbGEW5T…Q13i9ZZ4

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.

5.730 × 10⁹¹(92-digit number)

57309398895575727171…77586965465545845599

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

5.730 × 10⁹¹(92-digit number)

57309398895575727171…77586965465545845599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.730 × 10⁹¹(92-digit number)

57309398895575727171…77586965465545845601

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

1.146 × 10⁹²(93-digit number)

11461879779115145434…55173930931091691199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.146 × 10⁹²(93-digit number)

11461879779115145434…55173930931091691201

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

2.292 × 10⁹²(93-digit number)

22923759558230290868…10347861862183382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.292 × 10⁹²(93-digit number)

22923759558230290868…10347861862183382401

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

4.584 × 10⁹²(93-digit number)

45847519116460581736…20695723724366764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.584 × 10⁹²(93-digit number)

45847519116460581736…20695723724366764801

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

9.169 × 10⁹²(93-digit number)

91695038232921163473…41391447448733529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.169 × 10⁹²(93-digit number)

91695038232921163473…41391447448733529601

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

1.833 × 10⁹³(94-digit number)

18339007646584232694…82782894897467059199

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 #2,642,024

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