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Block #163,429

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/13/2013, 11:56:47 PM Β· Difficulty 9.8618 Β· 6,631,229 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ed0ba551702d74c6ec64a83bed8bbdb9cfdba33eb0690d1d40fe6c1698b25916
View on Chainz β†—

Height

#163,429

Difficulty

9.861785

Transactions

1

Size

199 B

Version

2

Bits

09dc9df5

Nonce

107,806

Timestamp

9/13/2013, 11:56:47 PM

Confirmations

6,631,229

Mined by

⛏️ P2SHAH8MuWecApb7HmsNwfd9UPDw7y2bVG62mK

Merkle Root

94ee4f098f41d2cb3df2bb18042152849fc6ef602c42bfdbeaa6b8f508e84616
Transactions (1)
Coinbase94ee4f098f41d2…a6b8f508e84616
1 in β†’ 1 out10.2700 XPM109 B
AH8MuWec…2bVG62mK
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.

3.919 Γ— 10⁹³(94-digit number)
39195261968465106454…49356246892347743549
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
3.919 Γ— 10⁹³(94-digit number)
39195261968465106454…49356246892347743549
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.919 Γ— 10⁹³(94-digit number)
39195261968465106454…49356246892347743551
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
7.839 Γ— 10⁹³(94-digit number)
78390523936930212909…98712493784695487099
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.839 Γ— 10⁹³(94-digit number)
78390523936930212909…98712493784695487101
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
1.567 Γ— 10⁹⁴(95-digit number)
15678104787386042581…97424987569390974199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.567 Γ— 10⁹⁴(95-digit number)
15678104787386042581…97424987569390974201
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
3.135 Γ— 10⁹⁴(95-digit number)
31356209574772085163…94849975138781948399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.135 Γ— 10⁹⁴(95-digit number)
31356209574772085163…94849975138781948401
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
6.271 Γ— 10⁹⁴(95-digit number)
62712419149544170327…89699950277563896799
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:57,601,312 XPMΒ·at block #6,794,657 Β· updates every 60s
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