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Block #2,092,371

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/29/2017, 4:46:28 AM Β· Difficulty 10.8713 Β· 4,734,344 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ad341c1bb1ff9cffd9b59fadaf76e5b71ffddd980b5c270500c1a587a49d6535
View on Chainz β†—

Height

#2,092,371

Difficulty

10.871262

Transactions

2

Size

1.69 KB

Version

2

Bits

0adf0b0e

Nonce

2,072,900,219

Timestamp

4/29/2017, 4:46:28 AM

Confirmations

4,734,344

Mined by

⛏️ P2SHATqhFeh2aHVqqoFjPXePCgxKkz9jcrGgPs

Merkle Root

3d1e581373d6aae6e2533584d270f50bf0a99282dc068b5dbb2322dc938c975a
Transactions (2)
Coinbase2ca424f8f67710…901352f6eea80f
1 in β†’ 1 out8.4800 XPM110 B
ATqhFeh2…9jcrGgPs
d87adfd0548701…47ee51d53b8d23
10 in β†’ 1 out549.1224 XPM1.49 KB
AMYNEfMP…qtivh1zM
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.

1.989 Γ— 10⁹⁴(95-digit number)
19894126400601044940…13291522978588246879
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
1.989 Γ— 10⁹⁴(95-digit number)
19894126400601044940…13291522978588246879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.989 Γ— 10⁹⁴(95-digit number)
19894126400601044940…13291522978588246881
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
3.978 Γ— 10⁹⁴(95-digit number)
39788252801202089880…26583045957176493759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.978 Γ— 10⁹⁴(95-digit number)
39788252801202089880…26583045957176493761
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
7.957 Γ— 10⁹⁴(95-digit number)
79576505602404179760…53166091914352987519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.957 Γ— 10⁹⁴(95-digit number)
79576505602404179760…53166091914352987521
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
1.591 Γ— 10⁹⁡(96-digit number)
15915301120480835952…06332183828705975039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.591 Γ— 10⁹⁡(96-digit number)
15915301120480835952…06332183828705975041
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
3.183 Γ— 10⁹⁡(96-digit number)
31830602240961671904…12664367657411950079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.183 Γ— 10⁹⁡(96-digit number)
31830602240961671904…12664367657411950081
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:57,857,873 XPMΒ·at block #6,826,714 Β· updates every 60s
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