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Block #3,086,685

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 3/10/2019, 9:29:38 AM Β· Difficulty 11.0382 Β· 3,751,498 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4b3e24b2cc2f120e6d31676fd98125ca976386c1a3d796fd9e629436bde4cdc3
View on Chainz β†—

Height

#3,086,685

Difficulty

11.038215

Transactions

2

Size

2.87 KB

Version

2

Bits

0b09c874

Nonce

762,466,907

Timestamp

3/10/2019, 9:29:38 AM

Confirmations

3,751,498

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

7b3bd6b1d67f542c9782158050b83285d2e442ccbc027ba017dc5ee89347c616
Transactions (2)
Coinbase8e1c972a29f4f9…11b3ad5dcf7e02
1 in β†’ 1 out8.2200 XPM110 B
AUhjokok…k5m93PZR
c1d7620d6e250d…05416d99dbc411
18 in β†’ 2 out3430.3948 XPM2.68 KB
AZQgL5kt…6NE43uZsAewYP7V7…VS6aSvKV
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.

3.995 Γ— 10⁹⁡(96-digit number)
39955068281317696960…79912718619026288639
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
3.995 Γ— 10⁹⁡(96-digit number)
39955068281317696960…79912718619026288639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.995 Γ— 10⁹⁡(96-digit number)
39955068281317696960…79912718619026288641
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
7.991 Γ— 10⁹⁡(96-digit number)
79910136562635393921…59825437238052577279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.991 Γ— 10⁹⁡(96-digit number)
79910136562635393921…59825437238052577281
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
1.598 Γ— 10⁹⁢(97-digit number)
15982027312527078784…19650874476105154559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.598 Γ— 10⁹⁢(97-digit number)
15982027312527078784…19650874476105154561
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
3.196 Γ— 10⁹⁢(97-digit number)
31964054625054157568…39301748952210309119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.196 Γ— 10⁹⁢(97-digit number)
31964054625054157568…39301748952210309121
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
6.392 Γ— 10⁹⁢(97-digit number)
63928109250108315137…78603497904420618239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.392 Γ— 10⁹⁢(97-digit number)
63928109250108315137…78603497904420618241
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
1.278 Γ— 10⁹⁷(98-digit number)
12785621850021663027…57206995808841236479
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:57,949,737 XPMΒ·at block #6,838,182 Β· updates every 60s
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