Block #3,242,744

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/27/2019, 4:35:40 AM · Difficulty 11.0075 · 3,596,663 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1a417591f03bd0b65642619db564c073bbf18f423c2095c87c24c3e6ae65b2a

View on Chainz ↗

Height

#3,242,744

Difficulty

11.007531

Transactions

Size

766 B

Version

Bits

0b01ed90

Nonce

1,825,700,649

Timestamp

6/27/2019, 4:35:40 AM

Confirmations

3,596,663

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

cd527dbd2ce46854e08a84969a0ed30dc281395aeb3ef256c225193f629832dd

Transactions (3)

Coinbase902c94dfc953ec…4e108b1cec220a

1 in → 1 out8.2600 XPM110 B

ASiq2qtK…VMhmk7yL

868d6f5699df48…1fea5f050fc497

2 in → 2 out12.4642 XPM340 B

AMjZ87GH…cvurqAXE ASiq2qtK…VMhmk7yL

952acf694d3d50…1145298b4c8706

1 in → 2 out4.2040 XPM226 B

ASiq2qtK…VMhmk7yL AJtQNmM4…XBRjaQ6m

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.

8.937 × 10⁹⁴(95-digit number)

89375549766248050451…75669358628747092859

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

8.937 × 10⁹⁴(95-digit number)

89375549766248050451…75669358628747092859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.937 × 10⁹⁴(95-digit number)

89375549766248050451…75669358628747092861

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

1.787 × 10⁹⁵(96-digit number)

17875109953249610090…51338717257494185719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.787 × 10⁹⁵(96-digit number)

17875109953249610090…51338717257494185721

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

3.575 × 10⁹⁵(96-digit number)

35750219906499220180…02677434514988371439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.575 × 10⁹⁵(96-digit number)

35750219906499220180…02677434514988371441

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

7.150 × 10⁹⁵(96-digit number)

71500439812998440361…05354869029976742879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.150 × 10⁹⁵(96-digit number)

71500439812998440361…05354869029976742881

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

1.430 × 10⁹⁶(97-digit number)

14300087962599688072…10709738059953485759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.430 × 10⁹⁶(97-digit number)

14300087962599688072…10709738059953485761

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

2.860 × 10⁹⁶(97-digit number)

28600175925199376144…21419476119906971519

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 #3,242,744

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