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Block #151,389

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2013, 3:53:05 PM Β· Difficulty 9.8603 Β· 6,661,276 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4dccdc269f18812ca3644e158e65f5b17b3513c7105f48b97447445de833500f
View on Chainz β†—

Height

#151,389

Difficulty

9.860271

Transactions

1

Size

198 B

Version

2

Bits

09dc3ab7

Nonce

46,084

Timestamp

9/5/2013, 3:53:05 PM

Confirmations

6,661,276

Mined by

⛏️ P2SHAKaGDwVVv7VLKh2cmLacAjw2bVh5Bk5GFu

Merkle Root

9cd3a2a75c746507ce901d886f0a5e6e136b2032faf2d6402e4806d25a6f4703
Transactions (1)
Coinbase9cd3a2a75c7465…4806d25a6f4703
1 in β†’ 1 out10.2700 XPM109 B
AKaGDwVV…h5Bk5GFu
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.

2.362 Γ— 10⁹³(94-digit number)
23626463574794936254…72815914798477536639
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
2.362 Γ— 10⁹³(94-digit number)
23626463574794936254…72815914798477536639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.362 Γ— 10⁹³(94-digit number)
23626463574794936254…72815914798477536641
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
4.725 Γ— 10⁹³(94-digit number)
47252927149589872509…45631829596955073279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.725 Γ— 10⁹³(94-digit number)
47252927149589872509…45631829596955073281
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
9.450 Γ— 10⁹³(94-digit number)
94505854299179745018…91263659193910146559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.450 Γ— 10⁹³(94-digit number)
94505854299179745018…91263659193910146561
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
1.890 Γ— 10⁹⁴(95-digit number)
18901170859835949003…82527318387820293119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.890 Γ— 10⁹⁴(95-digit number)
18901170859835949003…82527318387820293121
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
3.780 Γ— 10⁹⁴(95-digit number)
37802341719671898007…65054636775640586239
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:57,745,351 XPMΒ·at block #6,812,664 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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