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Block #161,904

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 11:09:01 PM Β· Difficulty 9.8607 Β· 6,632,614 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2baa4b4a53689dc206eb37b5f0b194e7b2cf03675a4d05d0ae966365652b7b2c
View on Chainz β†—

Height

#161,904

Difficulty

9.860670

Transactions

1

Size

198 B

Version

2

Bits

09dc54df

Nonce

22,448

Timestamp

9/12/2013, 11:09:01 PM

Confirmations

6,632,614

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

f07e247454557b4cd29f51a1aad1344d35915b65b02d34a57befd13ef5a0b8c4
Transactions (1)
Coinbasef07e247454557b…efd13ef5a0b8c4
1 in β†’ 1 out10.2700 XPM109 B
AX99MLNm…vtidqEwE
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.

1.352 Γ— 10⁹³(94-digit number)
13528185474283242822…49444050957091405599
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
1.352 Γ— 10⁹³(94-digit number)
13528185474283242822…49444050957091405599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.352 Γ— 10⁹³(94-digit number)
13528185474283242822…49444050957091405601
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
2.705 Γ— 10⁹³(94-digit number)
27056370948566485645…98888101914182811199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.705 Γ— 10⁹³(94-digit number)
27056370948566485645…98888101914182811201
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
5.411 Γ— 10⁹³(94-digit number)
54112741897132971291…97776203828365622399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.411 Γ— 10⁹³(94-digit number)
54112741897132971291…97776203828365622401
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
1.082 Γ— 10⁹⁴(95-digit number)
10822548379426594258…95552407656731244799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.082 Γ— 10⁹⁴(95-digit number)
10822548379426594258…95552407656731244801
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
2.164 Γ— 10⁹⁴(95-digit number)
21645096758853188516…91104815313462489599
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:57,600,182 XPMΒ·at block #6,794,517 Β· updates every 60s
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