Block #1,408,716

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/11/2016, 12:14:54 PM · Difficulty 10.8054 · 5,398,595 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ca3714c9f5783790ba12c51b2878ea52f35ff78a2f2b940d0ff2daf27040c32

View on Chainz ↗

Height

#1,408,716

Difficulty

10.805417

Transactions

Size

5.98 KB

Version

Bits

0ace2fc8

Nonce

956,941,168

Timestamp

1/11/2016, 12:14:54 PM

Confirmations

5,398,595

Mined by

⛏️ P2SHAPn9scTK2iBC9VNHXxshndozEtv5kjVH6V

Merkle Root

317c5b21603b2ab7a1db6a88046a808b963f4d4d4db5e62e069231976595fb8f

Transactions (3)

Coinbasea571abe3da4397…9a27ff20523e15

1 in → 1 out8.6300 XPM109 B

APn9scTK…v5kjVH6V

5ff603b223025e…8af580a77ccf4a

10 in → 2 out57.0110 XPM1.52 KB

AdvLfhqF…YUuRFQZL ATtUDFfT…z3o5khhK

58e82289df7c38…4bb4224e1825a8

29 in → 2 out110.4791 XPM4.26 KB

AZXhBoeT…yL6x46AU AcjqdNp6…HBMuoVXD

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.

4.758 × 10⁹⁶(97-digit number)

47589772440387104482…02091900301596835839

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

4.758 × 10⁹⁶(97-digit number)

47589772440387104482…02091900301596835839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.758 × 10⁹⁶(97-digit number)

47589772440387104482…02091900301596835841

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

9.517 × 10⁹⁶(97-digit number)

95179544880774208964…04183800603193671679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.517 × 10⁹⁶(97-digit number)

95179544880774208964…04183800603193671681

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

1.903 × 10⁹⁷(98-digit number)

19035908976154841792…08367601206387343359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.903 × 10⁹⁷(98-digit number)

19035908976154841792…08367601206387343361

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

3.807 × 10⁹⁷(98-digit number)

38071817952309683585…16735202412774686719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.807 × 10⁹⁷(98-digit number)

38071817952309683585…16735202412774686721

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

7.614 × 10⁹⁷(98-digit number)

76143635904619367171…33470404825549373439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.614 × 10⁹⁷(98-digit number)

76143635904619367171…33470404825549373441

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

1.522 × 10⁹⁸(99-digit number)

15228727180923873434…66940809651098746879

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 #1,408,716

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