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Block #2,232,812

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/1/2017, 9:13:20 PM Β· Difficulty 10.9461 Β· 4,604,155 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00a1f2a6c60b33d7114fde2eaa44072c65e5e599a72f8e799777dbf230c3a641
View on Chainz β†—

Height

#2,232,812

Difficulty

10.946076

Transactions

2

Size

1.28 KB

Version

2

Bits

0af2320a

Nonce

94,772,587

Timestamp

8/1/2017, 9:13:20 PM

Confirmations

4,604,155

Mined by

⛏️ P2SHAMh6tKBDizWwGNjpMhQvtJ29GLU9pVgjFv

Merkle Root

3070209cd6987af64fe31d6a93f17b4ac51860df92faa393629a47559bebf0f3
Transactions (2)
Coinbase0b720a4a5d1de9…ae798cb8b8ffdd
1 in β†’ 1 out8.3500 XPM110 B
AMh6tKBD…U9pVgjFv
e93ca98cb80504…918af934e40cc5
7 in β†’ 2 out5500.0000 XPM1.09 KB
AVg58jSY…UHr21FrvAdx7sHZn…u4ZprugG
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.

1.460 Γ— 10⁹⁴(95-digit number)
14603493125720042632…55102899086493524419
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
1.460 Γ— 10⁹⁴(95-digit number)
14603493125720042632…55102899086493524419
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.460 Γ— 10⁹⁴(95-digit number)
14603493125720042632…55102899086493524421
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
2.920 Γ— 10⁹⁴(95-digit number)
29206986251440085264…10205798172987048839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.920 Γ— 10⁹⁴(95-digit number)
29206986251440085264…10205798172987048841
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
5.841 Γ— 10⁹⁴(95-digit number)
58413972502880170529…20411596345974097679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.841 Γ— 10⁹⁴(95-digit number)
58413972502880170529…20411596345974097681
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
1.168 Γ— 10⁹⁡(96-digit number)
11682794500576034105…40823192691948195359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.168 Γ— 10⁹⁡(96-digit number)
11682794500576034105…40823192691948195361
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
2.336 Γ— 10⁹⁡(96-digit number)
23365589001152068211…81646385383896390719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.336 Γ— 10⁹⁡(96-digit number)
23365589001152068211…81646385383896390721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
4.673 Γ— 10⁹⁡(96-digit number)
46731178002304136423…63292770767792781439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,940,034 XPMΒ·at block #6,836,966 Β· updates every 60s
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