Block #2,646,065

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 4:39:35 AM · Difficulty 11.7441 · 4,190,848 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

71e0f02acfa8690f582b987689ee5a9eab9b3db390659ad282f24a4ecaca5e47

View on Chainz ↗

Height

#2,646,065

Difficulty

11.744056

Transactions

Size

1019 B

Version

Bits

0bbe7a7c

Nonce

904,384,536

Timestamp

5/3/2018, 4:39:35 AM

Confirmations

4,190,848

Mined by

⛏️ P2SHAR38cRU7784YE5Q3iJsTL1H89dbjNTFKmH

Merkle Root

e29344dc89858d5ece3d85790921fcdc5841f88a4bb1907f219ea4f292eb37c9

Transactions (2)

Coinbase23757443c45012…78e5cd49074648

1 in → 1 out7.2500 XPM110 B

AR38cRU7…bjNTFKmH

576ed0d7520b61…7624c5849e0006

5 in → 2 out621.7520 XPM818 B

ARJu8krJ…m6tCoLRj APeoPdwU…QfVCS1JE

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.

2.379 × 10⁹⁶(97-digit number)

23797135843659746498…98467720484524465919

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

2.379 × 10⁹⁶(97-digit number)

23797135843659746498…98467720484524465919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.379 × 10⁹⁶(97-digit number)

23797135843659746498…98467720484524465921

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

4.759 × 10⁹⁶(97-digit number)

47594271687319492997…96935440969048931839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.759 × 10⁹⁶(97-digit number)

47594271687319492997…96935440969048931841

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

9.518 × 10⁹⁶(97-digit number)

95188543374638985994…93870881938097863679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.518 × 10⁹⁶(97-digit number)

95188543374638985994…93870881938097863681

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

1.903 × 10⁹⁷(98-digit number)

19037708674927797198…87741763876195727359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.903 × 10⁹⁷(98-digit number)

19037708674927797198…87741763876195727361

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

3.807 × 10⁹⁷(98-digit number)

38075417349855594397…75483527752391454719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.807 × 10⁹⁷(98-digit number)

38075417349855594397…75483527752391454721

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

7.615 × 10⁹⁷(98-digit number)

76150834699711188795…50967055504782909439

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 #2,646,065

Cookie Preferences