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Block #161,059

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/12/2013, 9:45:03 AM Β· Difficulty 9.8595 Β· 6,642,235 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
533681dadfc55d7d33612221caad149755e1b255fdfae675a15506205aa54df1
View on Chainz β†—

Height

#161,059

Difficulty

9.859496

Transactions

1

Size

198 B

Version

2

Bits

09dc07e8

Nonce

6,795

Timestamp

9/12/2013, 9:45:03 AM

Confirmations

6,642,235

Mined by

⛏️ P2SHAX99MLNmm1FbkFRt6WY4Zu9rUBvtidqEwE

Merkle Root

827cbb7ccb690841900ee3b18e915cd319e9d29a2ed53ce3d1cfcc305aab7402
Transactions (1)
Coinbase827cbb7ccb6908…cfcc305aab7402
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.

4.538 Γ— 10⁹²(93-digit number)
45385842682487869177…47030606403077651629
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
4.538 Γ— 10⁹²(93-digit number)
45385842682487869177…47030606403077651629
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.538 Γ— 10⁹²(93-digit number)
45385842682487869177…47030606403077651631
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
9.077 Γ— 10⁹²(93-digit number)
90771685364975738354…94061212806155303259
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.077 Γ— 10⁹²(93-digit number)
90771685364975738354…94061212806155303261
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
1.815 Γ— 10⁹³(94-digit number)
18154337072995147670…88122425612310606519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.815 Γ— 10⁹³(94-digit number)
18154337072995147670…88122425612310606521
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
3.630 Γ— 10⁹³(94-digit number)
36308674145990295341…76244851224621213039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.630 Γ— 10⁹³(94-digit number)
36308674145990295341…76244851224621213041
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
7.261 Γ— 10⁹³(94-digit number)
72617348291980590683…52489702449242426079
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:57,670,378 XPMΒ·at block #6,803,293 Β· updates every 60s
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