Block #3,667,250

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2020, 12:13:44 AM · Difficulty 10.8838 · 3,136,930 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55a8bd19d1350b17cba65fb0e7e775aaa654be6dd347b6ed5ba7b5c30cb64bef

View on Chainz ↗

Height

#3,667,250

Difficulty

10.883804

Transactions

Size

2.83 KB

Version

Bits

0ae24102

Nonce

121,282,497

Timestamp

5/2/2020, 12:13:44 AM

Confirmations

3,136,930

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

65811f7bb1ada18f1d862b47ea013c7d26911f3d28891ca07d5cfc62f11aed0d

Transactions (5)

Coinbase7046278840e89b…7a0ee98d11c04f

1 in → 1 out8.4800 XPM110 B

ASiq2qtK…VMhmk7yL

ec2353c85e5189…431ca81c214ba3

12 in → 2 out101.2500 XPM1.41 KB

ASiq2qtK…VMhmk7yL AdGFnV3a…o6n2zX3x

66d09c7d30a173…89ad1c61dbb89c

3 in → 2 out25.3000 XPM420 B

ASiq2qtK…VMhmk7yL ASgJoPyT…Nqx4EoES

92481535aff3e1…b2201271e81dd8

2 in → 2 out16.8600 XPM307 B

ASiq2qtK…VMhmk7yL AWxHVeWs…Q7RMs542

341bef5d3bc669…0e79e2645bd45f

3 in → 2 out4.0600 XPM521 B

ANn2Zx9p…WKMq9Pta ASiq2qtK…VMhmk7yL

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.

7.546 × 10⁹⁷(98-digit number)

75465423528858132209…14144429636938997759

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

7.546 × 10⁹⁷(98-digit number)

75465423528858132209…14144429636938997759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.546 × 10⁹⁷(98-digit number)

75465423528858132209…14144429636938997761

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

1.509 × 10⁹⁸(99-digit number)

15093084705771626441…28288859273877995519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.509 × 10⁹⁸(99-digit number)

15093084705771626441…28288859273877995521

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

3.018 × 10⁹⁸(99-digit number)

30186169411543252883…56577718547755991039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.018 × 10⁹⁸(99-digit number)

30186169411543252883…56577718547755991041

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

6.037 × 10⁹⁸(99-digit number)

60372338823086505767…13155437095511982079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.037 × 10⁹⁸(99-digit number)

60372338823086505767…13155437095511982081

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

1.207 × 10⁹⁹(100-digit number)

12074467764617301153…26310874191023964159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.207 × 10⁹⁹(100-digit number)

12074467764617301153…26310874191023964161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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