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Block #75,096

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/21/2013, 2:36:56 PM Β· Difficulty 8.9959 Β· 6,730,057 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d2591599964c6f14f7eb592fd224ec8bb565cf52ed713e47cce7d5ac33d4f7d5
View on Chainz β†—

Height

#75,096

Difficulty

8.995908

Transactions

2

Size

359 B

Version

2

Bits

08fef3db

Nonce

262

Timestamp

7/21/2013, 2:36:56 PM

Confirmations

6,730,057

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

279bf54b15fd8ffb44100134343aa6e2b71fa91763868139a2f7dba53f7c60b9
Transactions (2)
Coinbased8f0af82ab6a67…26ebde90f5ce54
1 in β†’ 1 out12.3500 XPM110 B
AZDgU5ry…dmcwdqVC
9b2d46f48b7706…5bc8852711b616
1 in β†’ 1 out12.3400 XPM159 B
AW7xaLBs…KjHmcbd9
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.

2.995 Γ— 10⁹⁴(95-digit number)
29950149773850103398…54141345044226412919
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
2.995 Γ— 10⁹⁴(95-digit number)
29950149773850103398…54141345044226412919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.995 Γ— 10⁹⁴(95-digit number)
29950149773850103398…54141345044226412921
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
5.990 Γ— 10⁹⁴(95-digit number)
59900299547700206797…08282690088452825839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.990 Γ— 10⁹⁴(95-digit number)
59900299547700206797…08282690088452825841
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
1.198 Γ— 10⁹⁡(96-digit number)
11980059909540041359…16565380176905651679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.198 Γ— 10⁹⁡(96-digit number)
11980059909540041359…16565380176905651681
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
2.396 Γ— 10⁹⁡(96-digit number)
23960119819080082718…33130760353811303359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.396 Γ— 10⁹⁡(96-digit number)
23960119819080082718…33130760353811303361
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
4.792 Γ— 10⁹⁡(96-digit number)
47920239638160165437…66261520707622606719
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:57,685,291 XPMΒ·at block #6,805,152 Β· updates every 60s
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