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Block #2,214,752

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2017, 11:06:25 AM Β· Difficulty 10.9436 Β· 4,627,930 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
41dd6193d67cc09c3224d20afc3f4b9090afc7ebd11223f459e78e4b791296b2
View on Chainz β†—

Height

#2,214,752

Difficulty

10.943615

Transactions

1

Size

199 B

Version

2

Bits

0af190c7

Nonce

1,876,013,847

Timestamp

7/20/2017, 11:06:25 AM

Confirmations

4,627,930

Mined by

⛏️ P2SHAW7otfmaJVE8Tpuj9TaZo8yML74t1yynRx

Merkle Root

5de3bf77627e5d7521a94506da3ee9e4c888f840762840dab9def4b07f7a7874
Transactions (1)
Coinbase5de3bf77627e5d…def4b07f7a7874
1 in β†’ 1 out8.3400 XPM109 B
AW7otfma…4t1yynRx
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.

3.267 Γ— 10⁹⁴(95-digit number)
32677722661100803276…84644212442752266239
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
3.267 Γ— 10⁹⁴(95-digit number)
32677722661100803276…84644212442752266239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.267 Γ— 10⁹⁴(95-digit number)
32677722661100803276…84644212442752266241
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
6.535 Γ— 10⁹⁴(95-digit number)
65355445322201606552…69288424885504532479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.535 Γ— 10⁹⁴(95-digit number)
65355445322201606552…69288424885504532481
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
1.307 Γ— 10⁹⁡(96-digit number)
13071089064440321310…38576849771009064959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.307 Γ— 10⁹⁡(96-digit number)
13071089064440321310…38576849771009064961
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
2.614 Γ— 10⁹⁡(96-digit number)
26142178128880642620…77153699542018129919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.614 Γ— 10⁹⁡(96-digit number)
26142178128880642620…77153699542018129921
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
5.228 Γ— 10⁹⁡(96-digit number)
52284356257761285241…54307399084036259839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.228 Γ— 10⁹⁡(96-digit number)
52284356257761285241…54307399084036259841
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:57,985,802 XPMΒ·at block #6,842,681 Β· updates every 60s
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