Block #3,353,336

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/13/2019, 2:38:18 PM · Difficulty 10.9961 · 3,473,493 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ceedfcec358a5367dc500fc247ba2ba240473ab6685b512d7defbc5e00e0df7

View on Chainz ↗

Height

#3,353,336

Difficulty

10.996081

Transactions

Size

1.23 KB

Version

Bits

0afeff24

Nonce

563,200,142

Timestamp

9/13/2019, 2:38:18 PM

Confirmations

3,473,493

Mined by

⛏️ P2SHAQ5FiwjyjvhaytHAHXswZ1h3LBgz4RaTcb

Merkle Root

c667bea13e51d3da71616bccac0498e79979f7c1c912d81328b367d3ed860c78

Transactions (4)

Coinbaseb6b772d9f790d8…bd227384053964

1 in → 1 out8.2900 XPM109 B

AQ5Fiwjy…gz4RaTcb

002b112ddc82e2…f472dddbcdcb24

5 in → 2 out41.2500 XPM646 B

ASiq2qtK…VMhmk7yL AGbm9W17…Jvw6eg2t

f2937a13ce6e9a…1be6100fec119d

1 in → 2 out8.2400 XPM193 B

ASiq2qtK…VMhmk7yL AHRiuNWd…x34SS1Jh

54cc41717b9a95…9bdbb696ad09f1

1 in → 2 out4.2249 XPM225 B

ASiq2qtK…VMhmk7yL AadFZeqL…sPk6hBJP

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.

4.518 × 10⁹⁷(98-digit number)

45184969897521628839…57522298650776616959

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

4.518 × 10⁹⁷(98-digit number)

45184969897521628839…57522298650776616959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.518 × 10⁹⁷(98-digit number)

45184969897521628839…57522298650776616961

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

9.036 × 10⁹⁷(98-digit number)

90369939795043257679…15044597301553233919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.036 × 10⁹⁷(98-digit number)

90369939795043257679…15044597301553233921

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

1.807 × 10⁹⁸(99-digit number)

18073987959008651535…30089194603106467839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.807 × 10⁹⁸(99-digit number)

18073987959008651535…30089194603106467841

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

3.614 × 10⁹⁸(99-digit number)

36147975918017303071…60178389206212935679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.614 × 10⁹⁸(99-digit number)

36147975918017303071…60178389206212935681

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

7.229 × 10⁹⁸(99-digit number)

72295951836034606143…20356778412425871359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.229 × 10⁹⁸(99-digit number)

72295951836034606143…20356778412425871361

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

1.445 × 10⁹⁹(100-digit number)

14459190367206921228…40713556824851742719

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 #3,353,336

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