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Block #2,284,198

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/6/2017, 1:01:07 AM Β· Difficulty 10.9551 Β· 4,528,826 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e827d90ff21fd8387084591a37de7c133adb3d143cec8731ec64fbf3c4499f2e
View on Chainz β†—

Height

#2,284,198

Difficulty

10.955078

Transactions

2

Size

540 B

Version

2

Bits

0af47ff8

Nonce

57,347,963

Timestamp

9/6/2017, 1:01:07 AM

Confirmations

4,528,826

Mined by

⛏️ P2SHAGSxCgEn3J2jezREAUrKtHvLx49tRREGDP

Merkle Root

48593bd68fd93f28f51112c2fff1af351789bb6c9aeb7afbf6aeea8d374579ba
Transactions (2)
Coinbase345fd08cc403aa…2d1d2f17b27e63
1 in β†’ 1 out8.3300 XPM109 B
AGSxCgEn…9tRREGDP
e306eac87c90bf…94b02d82148461
2 in β†’ 1 out1999.9900 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.

5.246 Γ— 10⁹⁴(95-digit number)
52466436881291557257…69003826644248947679
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
5.246 Γ— 10⁹⁴(95-digit number)
52466436881291557257…69003826644248947679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.246 Γ— 10⁹⁴(95-digit number)
52466436881291557257…69003826644248947681
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
1.049 Γ— 10⁹⁡(96-digit number)
10493287376258311451…38007653288497895359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.049 Γ— 10⁹⁡(96-digit number)
10493287376258311451…38007653288497895361
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
2.098 Γ— 10⁹⁡(96-digit number)
20986574752516622903…76015306576995790719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.098 Γ— 10⁹⁡(96-digit number)
20986574752516622903…76015306576995790721
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
4.197 Γ— 10⁹⁡(96-digit number)
41973149505033245806…52030613153991581439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.197 Γ— 10⁹⁡(96-digit number)
41973149505033245806…52030613153991581441
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
8.394 Γ— 10⁹⁡(96-digit number)
83946299010066491612…04061226307983162879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.394 Γ— 10⁹⁡(96-digit number)
83946299010066491612…04061226307983162881
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:57,748,234 XPMΒ·at block #6,813,023 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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