Block #2,909,639

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/4/2018, 9:09:52 AM · Difficulty 11.5399 · 3,922,009 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a53e4142f0dc58de0422547997ca6177489c117c4812e6aae24057ac8f0c82db

View on Chainz ↗

Height

#2,909,639

Difficulty

11.539898

Transactions

Size

872 B

Version

Bits

0b8a36c5

Nonce

1,186,830,980

Timestamp

11/4/2018, 9:09:52 AM

Confirmations

3,922,009

Mined by

⛏️ P2SHALAWEgYYHDXYJSvmfKmKTzXb2sGzp1FFK2

Merkle Root

ab5e994e5c01fa04795a2d2cda6fe414538ae5a587a662778081be4fc4e5ff3f

Transactions (2)

Coinbase91fc6b9088f87c…da6c1ac8ba5691

1 in → 1 out7.5100 XPM110 B

ALAWEgYY…Gzp1FFK2

9606451c205e77…11f394ce98c976

4 in → 2 out305.4325 XPM670 B

AZhffMU7…Gtwmc2qz AHc2UgHR…T8V8px66

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.

5.551 × 10⁹⁸(99-digit number)

55519455692530712655…41849436000340213759

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

5.551 × 10⁹⁸(99-digit number)

55519455692530712655…41849436000340213759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.551 × 10⁹⁸(99-digit number)

55519455692530712655…41849436000340213761

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

1.110 × 10⁹⁹(100-digit number)

11103891138506142531…83698872000680427519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.110 × 10⁹⁹(100-digit number)

11103891138506142531…83698872000680427521

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

2.220 × 10⁹⁹(100-digit number)

22207782277012285062…67397744001360855039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.220 × 10⁹⁹(100-digit number)

22207782277012285062…67397744001360855041

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

4.441 × 10⁹⁹(100-digit number)

44415564554024570124…34795488002721710079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.441 × 10⁹⁹(100-digit number)

44415564554024570124…34795488002721710081

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

8.883 × 10⁹⁹(100-digit number)

88831129108049140248…69590976005443420159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.883 × 10⁹⁹(100-digit number)

88831129108049140248…69590976005443420161

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

1.776 × 10¹⁰⁰(101-digit number)

17766225821609828049…39181952010886840319

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 #2,909,639

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