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Block #2,297,170

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/15/2017, 1:51:49 PM Β· Difficulty 10.9482 Β· 4,517,129 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
39740d343aeec8df4adda5460a397c938ff435315cb405114327e33f33f35546
View on Chainz β†—

Height

#2,297,170

Difficulty

10.948224

Transactions

2

Size

426 B

Version

2

Bits

0af2becf

Nonce

679,216,892

Timestamp

9/15/2017, 1:51:49 PM

Confirmations

4,517,129

Mined by

⛏️ P2SHAZpMAr3hEFZ5oGTyUNg6z2UcodT1wGR3mz

Merkle Root

e3c62acd4e87346004c862591adcdae635c458fdf570e2e6302782967f96f5e4
Transactions (2)
Coinbase68f51756625e72…25e5f830bbf4a8
1 in β†’ 1 out8.3400 XPM110 B
AZpMAr3h…T1wGR3mz
5adee3f1d76aab…f66bcb1926e857
1 in β†’ 2 out31648.2752 XPM226 B
AXvZfEv9…emnUzf47AJ8c9Shn…GCZNE92R
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.

3.659 Γ— 10⁹⁴(95-digit number)
36597841756106680597…01159250318634819639
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
3.659 Γ— 10⁹⁴(95-digit number)
36597841756106680597…01159250318634819639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.659 Γ— 10⁹⁴(95-digit number)
36597841756106680597…01159250318634819641
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
7.319 Γ— 10⁹⁴(95-digit number)
73195683512213361194…02318500637269639279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.319 Γ— 10⁹⁴(95-digit number)
73195683512213361194…02318500637269639281
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
1.463 Γ— 10⁹⁡(96-digit number)
14639136702442672238…04637001274539278559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.463 Γ— 10⁹⁡(96-digit number)
14639136702442672238…04637001274539278561
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
2.927 Γ— 10⁹⁡(96-digit number)
29278273404885344477…09274002549078557119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.927 Γ— 10⁹⁡(96-digit number)
29278273404885344477…09274002549078557121
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
5.855 Γ— 10⁹⁡(96-digit number)
58556546809770688955…18548005098157114239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.855 Γ— 10⁹⁡(96-digit number)
58556546809770688955…18548005098157114241
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:57,758,456 XPMΒ·at block #6,814,298 Β· updates every 60s
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