Block #3,374,540

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/29/2019, 10:59:19 PM · Difficulty 10.9946 · 3,438,096 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f90531e57bfb945ce6be11bf03329d3053d064013f5b0c2db8db2f40b77240d7

View on Chainz ↗

Height

#3,374,540

Difficulty

10.994579

Transactions

Size

2.49 KB

Version

Bits

0afe9cb8

Nonce

154,351,384

Timestamp

9/29/2019, 10:59:19 PM

Confirmations

3,438,096

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

36b81e2e041ac44a47f7158a266279c7a47ccd3b73276e7a1aa8bcf8d3d37eb2

Transactions (5)

Coinbase04dc71511a04ea…4ef1909468a285

1 in → 1 out8.3100 XPM110 B

ASiq2qtK…VMhmk7yL

0e67905b33f53c…316faa714fb57c

13 in → 2 out100.1620 XPM1.56 KB

ASiq2qtK…VMhmk7yL ANWdJ2nc…BW7RisDk

041728f5ff73be…738dbeafa00eca

1 in → 2 out8.2900 XPM191 B

ASiq2qtK…VMhmk7yL ASSC3Jgq…tecLxMQL

c215bcb3660936…82e3df3c18a3ed

2 in → 2 out11.2800 XPM339 B

APVKWthF…PMMxwRoz AQiVoThn…s6Emvuqo

7ec9b157f003ce…8e6f6ffdcbd7aa

1 in → 2 out4.2667 XPM225 B

ASiq2qtK…VMhmk7yL AKpMPYXA…ia58Sytm

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.

4.031 × 10⁹⁵(96-digit number)

40310263408277280692…21781493035666636799

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

4.031 × 10⁹⁵(96-digit number)

40310263408277280692…21781493035666636799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.031 × 10⁹⁵(96-digit number)

40310263408277280692…21781493035666636801

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

8.062 × 10⁹⁵(96-digit number)

80620526816554561384…43562986071333273599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.062 × 10⁹⁵(96-digit number)

80620526816554561384…43562986071333273601

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

1.612 × 10⁹⁶(97-digit number)

16124105363310912276…87125972142666547199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.612 × 10⁹⁶(97-digit number)

16124105363310912276…87125972142666547201

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

3.224 × 10⁹⁶(97-digit number)

32248210726621824553…74251944285333094399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.224 × 10⁹⁶(97-digit number)

32248210726621824553…74251944285333094401

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

6.449 × 10⁹⁶(97-digit number)

64496421453243649107…48503888570666188799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.449 × 10⁹⁶(97-digit number)

64496421453243649107…48503888570666188801

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

1.289 × 10⁹⁷(98-digit number)

12899284290648729821…97007777141332377599

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 #3,374,540

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