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Block #163,546

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/14/2013, 1:51:39 AM Β· Difficulty 9.8618 Β· 6,643,202 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
94b9536da54446ec333fce86ee3e1bfb6211ae2600a520667b3d12066d0c75b4
View on Chainz β†—

Height

#163,546

Difficulty

9.861816

Transactions

1

Size

199 B

Version

2

Bits

09dc9ff3

Nonce

38,020

Timestamp

9/14/2013, 1:51:39 AM

Confirmations

6,643,202

Mined by

⛏️ P2SHAHiscA3WFz9dnGf3xRFCFqJkKatvPD5RmV

Merkle Root

2f39bda247bfa761a24858089287b954ef107974a9e4f0c19f3f3132915496b3
Transactions (1)
Coinbase2f39bda247bfa7…3f3132915496b3
1 in β†’ 1 out10.2700 XPM109 B
AHiscA3W…tvPD5RmV
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.

6.938 Γ— 10⁹⁴(95-digit number)
69389267712537668826…53894272648910607879
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
6.938 Γ— 10⁹⁴(95-digit number)
69389267712537668826…53894272648910607879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.938 Γ— 10⁹⁴(95-digit number)
69389267712537668826…53894272648910607881
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
1.387 Γ— 10⁹⁡(96-digit number)
13877853542507533765…07788545297821215759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.387 Γ— 10⁹⁡(96-digit number)
13877853542507533765…07788545297821215761
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
2.775 Γ— 10⁹⁡(96-digit number)
27755707085015067530…15577090595642431519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.775 Γ— 10⁹⁡(96-digit number)
27755707085015067530…15577090595642431521
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
5.551 Γ— 10⁹⁡(96-digit number)
55511414170030135060…31154181191284863039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.551 Γ— 10⁹⁡(96-digit number)
55511414170030135060…31154181191284863041
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
1.110 Γ— 10⁹⁢(97-digit number)
11102282834006027012…62308362382569726079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,698,082 XPMΒ·at block #6,806,747 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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