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Block #160,041

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/11/2013, 3:11:41 PM Β· Difficulty 9.8622 Β· 6,645,571 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
652c682f700c1866ff0387b7451e12924aa141f1cea550f79aab81a669ee12cb
View on Chainz β†—

Height

#160,041

Difficulty

9.862224

Transactions

1

Size

197 B

Version

2

Bits

09dcbab7

Nonce

1,062,667

Timestamp

9/11/2013, 3:11:41 PM

Confirmations

6,645,571

Mined by

⛏️ P2SHAWbm4AWfhyZEMkdPYLMs4FyYdBzNGrUw91

Merkle Root

1d84b1bf5e0b8ffa08bd5922c5a326f68ebcae356e94a328b0f29046719dcbab
Transactions (1)
Coinbase1d84b1bf5e0b8f…f29046719dcbab
1 in β†’ 1 out10.2700 XPM109 B
AWbm4AWf…zNGrUw91
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.

1.142 Γ— 10⁹⁰(91-digit number)
11428542728710612164…88229419795969591839
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
1.142 Γ— 10⁹⁰(91-digit number)
11428542728710612164…88229419795969591839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.142 Γ— 10⁹⁰(91-digit number)
11428542728710612164…88229419795969591841
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
2.285 Γ— 10⁹⁰(91-digit number)
22857085457421224328…76458839591939183679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.285 Γ— 10⁹⁰(91-digit number)
22857085457421224328…76458839591939183681
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
4.571 Γ— 10⁹⁰(91-digit number)
45714170914842448656…52917679183878367359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.571 Γ— 10⁹⁰(91-digit number)
45714170914842448656…52917679183878367361
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
9.142 Γ— 10⁹⁰(91-digit number)
91428341829684897313…05835358367756734719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.142 Γ— 10⁹⁰(91-digit number)
91428341829684897313…05835358367756734721
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
1.828 Γ— 10⁹¹(92-digit number)
18285668365936979462…11670716735513469439
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:57,688,970 XPMΒ·at block #6,805,611 Β· updates every 60s
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