Block #1,638,089

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/20/2016, 3:02:32 PM · Difficulty 10.6815 · 5,179,431 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

236f9bb30e5435b80ab3be7ef53984b60e5dd48cf7bcbb332e9a04e30dcbbaea

View on Chainz ↗

Height

#1,638,089

Difficulty

10.681547

Transactions

Size

1.14 KB

Version

Bits

0aae79e3

Nonce

722,960,701

Timestamp

6/20/2016, 3:02:32 PM

Confirmations

5,179,431

Mined by

⛏️ P2SHAMXwuz1bzw6qcxJHdS7ynPtsxLkybp3Nv3

Merkle Root

c7827e0bd4b0327b683780569f333092e89e59c5e6890b111b7b551f3a63d014

Transactions (2)

Coinbasec1fbf992c1027b…4417fd14fa06b1

1 in → 1 out8.7600 XPM110 B

AMXwuz1b…kybp3Nv3

2bcf97e00d5864…76eb301317d086

6 in → 2 out44.6537 XPM967 B

AYJ8RsRn…ECjBJ413 AWLnwpxa…oGjZgZDj

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.

3.818 × 10⁹⁴(95-digit number)

38182991563106464848…14826982759721192879

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

3.818 × 10⁹⁴(95-digit number)

38182991563106464848…14826982759721192879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.818 × 10⁹⁴(95-digit number)

38182991563106464848…14826982759721192881

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

7.636 × 10⁹⁴(95-digit number)

76365983126212929697…29653965519442385759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.636 × 10⁹⁴(95-digit number)

76365983126212929697…29653965519442385761

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

1.527 × 10⁹⁵(96-digit number)

15273196625242585939…59307931038884771519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.527 × 10⁹⁵(96-digit number)

15273196625242585939…59307931038884771521

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

3.054 × 10⁹⁵(96-digit number)

30546393250485171879…18615862077769543039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.054 × 10⁹⁵(96-digit number)

30546393250485171879…18615862077769543041

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

6.109 × 10⁹⁵(96-digit number)

61092786500970343758…37231724155539086079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.109 × 10⁹⁵(96-digit number)

61092786500970343758…37231724155539086081

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

Block #1,638,089

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