Block #2,641,187

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/1/2018, 6:35:49 AM · Difficulty 11.6106 · 4,195,157 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c24d043e080a9a77b23ab8de6ba27520a9bb8e8185f083f9639bef5b27cf8f90

View on Chainz ↗

Height

#2,641,187

Difficulty

11.610573

Transactions

Size

2.73 KB

Version

Bits

0b9c4e86

Nonce

564,122,501

Timestamp

5/1/2018, 6:35:49 AM

Confirmations

4,195,157

Mined by

⛏️ P2SHARyQvwFGBVQapxAUYbppLkBP7stRZoRH3e

Merkle Root

ee2602b50e421227bc35d65cc3d91595388964f57a035653838177fb6bcb0d7d

Transactions (5)

Coinbaseaeb634095e2979…53e3b637e2e85f

1 in → 1 out7.4600 XPM110 B

ARyQvwFG…tRZoRH3e

bb8d08cbd41c51…e5ece8516d7f69

1 in → 2 out2504.8580 XPM226 B

AetJjm2t…juC9mynR AV4Hs6Hs…F2VCBNgj

7d3fc8313fbd86…605ec331e2f3e9

9 in → 2 out51.8899 XPM1.18 KB

AWp4iAg7…FUBLEm8x ARdfEHwY…UzdMBq2F

7fd880dbfa9ab4…5738ab192c98ec

2 in → 2 out10.2868 XPM339 B

AGpNcnjX…ExiscN2C AM8zypoq…cJ83iQ9D

ab946a1288c322…0e12a92381293a

5 in → 2 out1.0583 XPM821 B

AcTtMaX7…Mtj23yYJ AWANEXAN…BEokc467

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.

5.014 × 10⁹⁵(96-digit number)

50142521283445105184…23263188530109945599

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

5.014 × 10⁹⁵(96-digit number)

50142521283445105184…23263188530109945599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.014 × 10⁹⁵(96-digit number)

50142521283445105184…23263188530109945601

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

1.002 × 10⁹⁶(97-digit number)

10028504256689021036…46526377060219891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.002 × 10⁹⁶(97-digit number)

10028504256689021036…46526377060219891201

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

2.005 × 10⁹⁶(97-digit number)

20057008513378042073…93052754120439782399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.005 × 10⁹⁶(97-digit number)

20057008513378042073…93052754120439782401

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

4.011 × 10⁹⁶(97-digit number)

40114017026756084147…86105508240879564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.011 × 10⁹⁶(97-digit number)

40114017026756084147…86105508240879564801

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

8.022 × 10⁹⁶(97-digit number)

80228034053512168294…72211016481759129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.022 × 10⁹⁶(97-digit number)

80228034053512168294…72211016481759129601

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

1.604 × 10⁹⁷(98-digit number)

16045606810702433658…44422032963518259199

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.604 × 10⁹⁷(98-digit number)

16045606810702433658…44422032963518259201

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 #2,641,187

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