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Block #2,924,027

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/15/2018, 1:03:59 PM Β· Difficulty 11.3580 Β· 3,909,707 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
83ae193224335cd499da06660f366d94a6d9856b5142c3a5f3d739246e62260b
View on Chainz β†—

Height

#2,924,027

Difficulty

11.358035

Transactions

2

Size

1.57 KB

Version

2

Bits

0b5ba82a

Nonce

449,212,841

Timestamp

11/15/2018, 1:03:59 PM

Confirmations

3,909,707

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

43e1a5028c1bacb4782b92ffc1da02abe354c3cc3dd98bfdc9def7bc3a625c0f
Transactions (2)
Coinbase65254cce723459…766a502cfc21d2
1 in β†’ 1 out7.7600 XPM110 B
AbXwmGxD…4XXYP765
8c0ef16a71a275…e8f0bda9665acf
9 in β†’ 2 out18.1000 XPM1.38 KB
AJgMrEpx…feT4viBKAQ38x2c7…fnwZaV8K
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.

8.835 Γ— 10⁹⁴(95-digit number)
88350479531223707553…69027977776605453199
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
8.835 Γ— 10⁹⁴(95-digit number)
88350479531223707553…69027977776605453199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.835 Γ— 10⁹⁴(95-digit number)
88350479531223707553…69027977776605453201
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
1.767 Γ— 10⁹⁡(96-digit number)
17670095906244741510…38055955553210906399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.767 Γ— 10⁹⁡(96-digit number)
17670095906244741510…38055955553210906401
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
3.534 Γ— 10⁹⁡(96-digit number)
35340191812489483021…76111911106421812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.534 Γ— 10⁹⁡(96-digit number)
35340191812489483021…76111911106421812801
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
7.068 Γ— 10⁹⁡(96-digit number)
70680383624978966042…52223822212843625599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.068 Γ— 10⁹⁡(96-digit number)
70680383624978966042…52223822212843625601
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
1.413 Γ— 10⁹⁢(97-digit number)
14136076724995793208…04447644425687251199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.413 Γ— 10⁹⁢(97-digit number)
14136076724995793208…04447644425687251201
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
2.827 Γ— 10⁹⁢(97-digit number)
28272153449991586417…08895288851374502399
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:57,914,096 XPMΒ·at block #6,833,733 Β· updates every 60s
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