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Block #237,752

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/1/2013, 5:19:25 AM Β· Difficulty 9.9505 Β· 6,570,639 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
001f0b2daa56039a6390376be9ba03ccb8e86c20bd669870edff195418b69508
View on Chainz β†—

Height

#237,752

Difficulty

9.950489

Transactions

1

Size

198 B

Version

2

Bits

09f35337

Nonce

41,112

Timestamp

11/1/2013, 5:19:25 AM

Confirmations

6,570,639

Mined by

⛏️ P2SHAZnPYg8XCxcZrU372xpdUULdGsaL9G3mAi

Merkle Root

2e3dff4ba1ae94b8aec5a295b60efe10f85bb301f18f0e180994bc8a95bb335f
Transactions (1)
Coinbase2e3dff4ba1ae94…94bc8a95bb335f
1 in β†’ 1 out10.0800 XPM109 B
AZnPYg8X…aL9G3mAi
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.

1.889 Γ— 10⁹³(94-digit number)
18897194904563105379…40112038895857711999
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
1.889 Γ— 10⁹³(94-digit number)
18897194904563105379…40112038895857711999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.889 Γ— 10⁹³(94-digit number)
18897194904563105379…40112038895857712001
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
3.779 Γ— 10⁹³(94-digit number)
37794389809126210759…80224077791715423999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.779 Γ— 10⁹³(94-digit number)
37794389809126210759…80224077791715424001
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
7.558 Γ— 10⁹³(94-digit number)
75588779618252421518…60448155583430847999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.558 Γ— 10⁹³(94-digit number)
75588779618252421518…60448155583430848001
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
1.511 Γ— 10⁹⁴(95-digit number)
15117755923650484303…20896311166861695999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.511 Γ— 10⁹⁴(95-digit number)
15117755923650484303…20896311166861696001
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
3.023 Γ— 10⁹⁴(95-digit number)
30235511847300968607…41792622333723391999
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:57,711,184 XPMΒ·at block #6,808,390 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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