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Block #1,748,009

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2016, 6:21:15 PM Β· Difficulty 10.7031 Β· 5,085,913 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e478908ab43607c4d450accbde90eba5630c020cfdcda97a7403d51b47d2b2f9
View on Chainz β†—

Height

#1,748,009

Difficulty

10.703126

Transactions

1

Size

199 B

Version

2

Bits

0ab4000b

Nonce

515,073,322

Timestamp

9/4/2016, 6:21:15 PM

Confirmations

5,085,913

Mined by

⛏️ P2SHAb48hFMW7xyFouJh5bmJWDhvFHRrVkegFF

Merkle Root

31332539ab9dd1134c6f70df3b9a70b3b002e25d43d1c853aa648c70ad9f34de
Transactions (1)
Coinbase31332539ab9dd1…648c70ad9f34de
1 in β†’ 1 out8.7200 XPM109 B
Ab48hFMW…RrVkegFF
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.

1.132 Γ— 10⁹⁡(96-digit number)
11320572281341193209…62476545689553172159
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
1.132 Γ— 10⁹⁡(96-digit number)
11320572281341193209…62476545689553172159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.132 Γ— 10⁹⁡(96-digit number)
11320572281341193209…62476545689553172161
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
2.264 Γ— 10⁹⁡(96-digit number)
22641144562682386418…24953091379106344319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.264 Γ— 10⁹⁡(96-digit number)
22641144562682386418…24953091379106344321
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
4.528 Γ— 10⁹⁡(96-digit number)
45282289125364772837…49906182758212688639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.528 Γ— 10⁹⁡(96-digit number)
45282289125364772837…49906182758212688641
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
9.056 Γ— 10⁹⁡(96-digit number)
90564578250729545674…99812365516425377279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.056 Γ— 10⁹⁡(96-digit number)
90564578250729545674…99812365516425377281
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
1.811 Γ— 10⁹⁢(97-digit number)
18112915650145909134…99624731032850754559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.811 Γ— 10⁹⁢(97-digit number)
18112915650145909134…99624731032850754561
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:57,915,603 XPMΒ·at block #6,833,921 Β· updates every 60s
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