Block #2,639,314

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/30/2018, 2:44:43 PM · Difficulty 11.5323 · 4,200,769 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ac15ca74ffdab2d5288b8e2de65dc4c8d30263b21d4a834778f4f49b3610db9

View on Chainz ↗

Height

#2,639,314

Difficulty

11.532306

Transactions

Size

947 B

Version

Bits

0b88452e

Nonce

443,855,179

Timestamp

4/30/2018, 2:44:43 PM

Confirmations

4,200,769

Mined by

⛏️ P2SHAXBZszqHc1UjSo5CE5UjWUgXnYsV7XshTt

Merkle Root

073046b4f2c2965eb9104a8203da877d403f960e208041d9216258c9213e5a0f

Transactions (3)

Coinbasea88526f517d183…3c1fcc9a90d4e5

1 in → 1 out7.5300 XPM110 B

AXBZszqH…sV7XshTt

e1ce51cad26e47…a3c3e113c9340d

3 in → 2 out167.1331 XPM520 B

AZ9BUr5M…2kr8KhjV AJ3NJZPt…zZAzxYEX

625964f10cad7c…87e6f061d40b6e

1 in → 2 out2.1382 XPM226 B

Adn2P4Jc…8Po7jS1Q AJ7T6oAS…wVuMVHSV

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.

1.432 × 10⁹⁶(97-digit number)

14322702541405853705…35158400220608958399

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

1.432 × 10⁹⁶(97-digit number)

14322702541405853705…35158400220608958399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.432 × 10⁹⁶(97-digit number)

14322702541405853705…35158400220608958401

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

2.864 × 10⁹⁶(97-digit number)

28645405082811707411…70316800441217916799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.864 × 10⁹⁶(97-digit number)

28645405082811707411…70316800441217916801

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

5.729 × 10⁹⁶(97-digit number)

57290810165623414822…40633600882435833599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.729 × 10⁹⁶(97-digit number)

57290810165623414822…40633600882435833601

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

1.145 × 10⁹⁷(98-digit number)

11458162033124682964…81267201764871667199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.145 × 10⁹⁷(98-digit number)

11458162033124682964…81267201764871667201

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

2.291 × 10⁹⁷(98-digit number)

22916324066249365929…62534403529743334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.291 × 10⁹⁷(98-digit number)

22916324066249365929…62534403529743334401

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

4.583 × 10⁹⁷(98-digit number)

45832648132498731858…25068807059486668799

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 #2,639,314

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