Block #1,840,632

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/8/2016, 7:17:03 PM · Difficulty 10.6410 · 4,990,485 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

829410bcdb2423dc03deb646b11d8416cb2fb4b2bf1b48486d13ae1bb68b0157

View on Chainz ↗

Height

#1,840,632

Difficulty

10.640967

Transactions

Size

3.45 KB

Version

Bits

0aa4166a

Nonce

974,981,296

Timestamp

11/8/2016, 7:17:03 PM

Confirmations

4,990,485

Mined by

⛏️ P2SHAN1sUduC4zyaGPRRUpeKijQJd9h8fcNUcS

Merkle Root

8404526e9d8e35ff16c0706bbcaa78a1a4df657b502aa740fec1fefa7472ddcf

Transactions (2)

Coinbase00921e501cfdca…20ed8dc75144d5

1 in → 1 out8.8600 XPM109 B

AN1sUduC…h8fcNUcS

cdc65b236dedd6…96a764fbf9360f

22 in → 2 out182.8825 XPM3.26 KB

AMAMJURH…AHEdVV8M AcdVU5yx…QVsWFgWB

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.

1.979 × 10⁹⁶(97-digit number)

19793255732003800922…76524051751729126399

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

1.979 × 10⁹⁶(97-digit number)

19793255732003800922…76524051751729126399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.979 × 10⁹⁶(97-digit number)

19793255732003800922…76524051751729126401

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

3.958 × 10⁹⁶(97-digit number)

39586511464007601845…53048103503458252799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.958 × 10⁹⁶(97-digit number)

39586511464007601845…53048103503458252801

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

7.917 × 10⁹⁶(97-digit number)

79173022928015203691…06096207006916505599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.917 × 10⁹⁶(97-digit number)

79173022928015203691…06096207006916505601

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

1.583 × 10⁹⁷(98-digit number)

15834604585603040738…12192414013833011199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.583 × 10⁹⁷(98-digit number)

15834604585603040738…12192414013833011201

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

3.166 × 10⁹⁷(98-digit number)

31669209171206081476…24384828027666022399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.166 × 10⁹⁷(98-digit number)

31669209171206081476…24384828027666022401

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

6.333 × 10⁹⁷(98-digit number)

63338418342412162953…48769656055332044799

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 #1,840,632

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