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Block #1,823,530

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/25/2016, 11:40:04 AM Β· Difficulty 10.8206 Β· 4,987,102 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
da0989ba9cded73c3532a3baa5ad726eb46cb67a8086abd3c1f3d58f5c2e7f27
View on Chainz β†—

Height

#1,823,530

Difficulty

10.820556

Transactions

2

Size

1.57 KB

Version

2

Bits

0ad20ff0

Nonce

1,552,470,466

Timestamp

10/25/2016, 11:40:04 AM

Confirmations

4,987,102

Mined by

⛏️ P2SHAHbww413JGHUpyViigDH8g9ikuUKLrTzdx

Merkle Root

7cd8a57c8af1fb35f8696560e590b6f5f837be08cac9979d10881ad6343c5506
Transactions (2)
Coinbase261bc5b779bcb9…ebc07d32ba6811
1 in β†’ 1 out8.5500 XPM109 B
AHbww413…UKLrTzdx
08f7946be766d6…a9b23e80be910c
9 in β†’ 2 out50000.0100 XPM1.38 KB
AJ3jgjnC…fuAhBk2vAYKArr5V…V9VqiqCZ
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.073 Γ— 10⁹⁴(95-digit number)
80736349371768307229…20303561626858388959
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
8.073 Γ— 10⁹⁴(95-digit number)
80736349371768307229…20303561626858388959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.073 Γ— 10⁹⁴(95-digit number)
80736349371768307229…20303561626858388961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.614 Γ— 10⁹⁡(96-digit number)
16147269874353661445…40607123253716777919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.614 Γ— 10⁹⁡(96-digit number)
16147269874353661445…40607123253716777921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
3.229 Γ— 10⁹⁡(96-digit number)
32294539748707322891…81214246507433555839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.229 Γ— 10⁹⁡(96-digit number)
32294539748707322891…81214246507433555841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
6.458 Γ— 10⁹⁡(96-digit number)
64589079497414645783…62428493014867111679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.458 Γ— 10⁹⁡(96-digit number)
64589079497414645783…62428493014867111681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.291 Γ— 10⁹⁢(97-digit number)
12917815899482929156…24856986029734223359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.291 Γ— 10⁹⁢(97-digit number)
12917815899482929156…24856986029734223361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,729,143 XPMΒ·at block #6,810,631 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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