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Block #2,284,219

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2017, 1:22:10 AM Β· Difficulty 10.9551 Β· 4,532,265 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
54221fb74a3c9044bf97eeaf860296caa0625929c8185adfb7e4dda490a3fbef
View on Chainz β†—

Height

#2,284,219

Difficulty

10.955052

Transactions

2

Size

542 B

Version

2

Bits

0af47e45

Nonce

412,624,523

Timestamp

9/6/2017, 1:22:10 AM

Confirmations

4,532,265

Mined by

⛏️ P2SHAXAr67MsGT8JepPg5dVStJyiR5xdWBhm6g

Merkle Root

0a14656fc9f1042d2e73c05f9476de9e7aa05be20d5dedb86ec0129ade3e9987
Transactions (2)
Coinbase848daa551dd291…5ae9290cb02f70
1 in β†’ 1 out8.3300 XPM110 B
AXAr67Ms…xdWBhm6g
7a780c8959dba2…489c3c9fd42605
2 in β†’ 1 out2499.9900 XPM341 B
AcxhUhX6…N8N8w2tm
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.

2.096 Γ— 10⁹⁷(98-digit number)
20969866193565226011…47256239347305021439
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
2.096 Γ— 10⁹⁷(98-digit number)
20969866193565226011…47256239347305021439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.096 Γ— 10⁹⁷(98-digit number)
20969866193565226011…47256239347305021441
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
4.193 Γ— 10⁹⁷(98-digit number)
41939732387130452023…94512478694610042879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.193 Γ— 10⁹⁷(98-digit number)
41939732387130452023…94512478694610042881
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
8.387 Γ— 10⁹⁷(98-digit number)
83879464774260904047…89024957389220085759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.387 Γ— 10⁹⁷(98-digit number)
83879464774260904047…89024957389220085761
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
1.677 Γ— 10⁹⁸(99-digit number)
16775892954852180809…78049914778440171519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.677 Γ— 10⁹⁸(99-digit number)
16775892954852180809…78049914778440171521
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
3.355 Γ— 10⁹⁸(99-digit number)
33551785909704361619…56099829556880343039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.355 Γ— 10⁹⁸(99-digit number)
33551785909704361619…56099829556880343041
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:57,775,998 XPMΒ·at block #6,816,483 Β· updates every 60s
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