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Block #939,458

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/16/2015, 9:32:27 PM Β· Difficulty 10.9007 Β· 5,874,539 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d7bb5770209afd7815901e8af2a09fa2a686a07dbcd5cfbb2f0d005d0d710839
View on Chainz β†—

Height

#939,458

Difficulty

10.900741

Transactions

2

Size

15.31 KB

Version

2

Bits

0ae696fe

Nonce

1,694,952,294

Timestamp

2/16/2015, 9:32:27 PM

Confirmations

5,874,539

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

45bca8ef7da6418a8863419f6c21ad348da165580f3e20e21414c1c83f64663d
Transactions (2)
Coinbase3204f844adf529…ec380da5420dba
1 in β†’ 1 out8.5600 XPM116 B
ANSXnLY2…Sd25TjkD
20a7e6b202bf66…42969c04938853
104 in β†’ 2 out500.2885 XPM15.11 KB
AYRU38aU…DqMwcwN4AJjnK9uC…VreFquR4
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.

1.674 Γ— 10⁹⁡(96-digit number)
16744603328365669594…74625469075867067159
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
1.674 Γ— 10⁹⁡(96-digit number)
16744603328365669594…74625469075867067159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.674 Γ— 10⁹⁡(96-digit number)
16744603328365669594…74625469075867067161
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
3.348 Γ— 10⁹⁡(96-digit number)
33489206656731339188…49250938151734134319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.348 Γ— 10⁹⁡(96-digit number)
33489206656731339188…49250938151734134321
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
6.697 Γ— 10⁹⁡(96-digit number)
66978413313462678377…98501876303468268639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.697 Γ— 10⁹⁡(96-digit number)
66978413313462678377…98501876303468268641
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
1.339 Γ— 10⁹⁢(97-digit number)
13395682662692535675…97003752606936537279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.339 Γ— 10⁹⁢(97-digit number)
13395682662692535675…97003752606936537281
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
2.679 Γ— 10⁹⁢(97-digit number)
26791365325385071350…94007505213873074559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.679 Γ— 10⁹⁢(97-digit number)
26791365325385071350…94007505213873074561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,756,057 XPMΒ·at block #6,813,996 Β· updates every 60s
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