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Block #2,796,486

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/16/2018, 11:53:00 AM Β· Difficulty 11.6795 Β· 4,046,747 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0350edec46e6213e429bba5301b8c662187eb841af1eb11005c088a5e4de667e
View on Chainz β†—

Height

#2,796,486

Difficulty

11.679527

Transactions

1

Size

202 B

Version

2

Bits

0badf574

Nonce

1,069,818,385

Timestamp

8/16/2018, 11:53:00 AM

Confirmations

4,046,747

Mined by

⛏️ P2SHAab6APHB5tta8eQB5Ex4PdgkwrSFEVq2ZF

Merkle Root

fbc13bb6dea2f2e97217f2e738ac8e5945577ebf2d95e87f173b4365ea0f5f88
Transactions (1)
Coinbasefbc13bb6dea2f2…3b4365ea0f5f88
1 in β†’ 1 out7.3200 XPM110 B
Aab6APHB…SFEVq2ZF
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.

6.264 Γ— 10⁹⁸(99-digit number)
62645161551176070374…76838985684007649279
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
6.264 Γ— 10⁹⁸(99-digit number)
62645161551176070374…76838985684007649279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.264 Γ— 10⁹⁸(99-digit number)
62645161551176070374…76838985684007649281
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
1.252 Γ— 10⁹⁹(100-digit number)
12529032310235214074…53677971368015298559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.252 Γ— 10⁹⁹(100-digit number)
12529032310235214074…53677971368015298561
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
2.505 Γ— 10⁹⁹(100-digit number)
25058064620470428149…07355942736030597119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.505 Γ— 10⁹⁹(100-digit number)
25058064620470428149…07355942736030597121
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
5.011 Γ— 10⁹⁹(100-digit number)
50116129240940856299…14711885472061194239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.011 Γ— 10⁹⁹(100-digit number)
50116129240940856299…14711885472061194241
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
1.002 Γ— 10¹⁰⁰(101-digit number)
10023225848188171259…29423770944122388479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.002 Γ— 10¹⁰⁰(101-digit number)
10023225848188171259…29423770944122388481
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
2.004 Γ— 10¹⁰⁰(101-digit number)
20046451696376342519…58847541888244776959
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:57,990,239 XPMΒ·at block #6,843,232 Β· updates every 60s
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