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Block #3,233,069

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/20/2019, 7:22:27 AM Β· Difficulty 11.0002 Β· 3,600,436 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9265fd37b62b20dc78055d8acf339fe49084b75439b1659d70244ec3fc86d9e9
View on Chainz β†—

Height

#3,233,069

Difficulty

11.000173

Transactions

2

Size

576 B

Version

2

Bits

0b000b52

Nonce

1,582,628,949

Timestamp

6/20/2019, 7:22:27 AM

Confirmations

3,600,436

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

da8db1459c5aae76e855fd24de4f61f6c9d08bb1a1c8cf43e6bdcee073d38500
Transactions (2)
Coinbase2b1a3cbdb1a636…0d61fac3413677
1 in β†’ 1 out8.2600 XPM110 B
AbXwmGxD…4XXYP765
26b18b1b8c6686…b77d3509842b3f
2 in β†’ 2 out18.9427 XPM375 B
AeTHTL7A…vT1872bkAKNpDQD6…j3iPmYAk
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.

6.337 Γ— 10⁹⁷(98-digit number)
63371939718744527357…26773614387868303359
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
6.337 Γ— 10⁹⁷(98-digit number)
63371939718744527357…26773614387868303359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.337 Γ— 10⁹⁷(98-digit number)
63371939718744527357…26773614387868303361
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
1.267 Γ— 10⁹⁸(99-digit number)
12674387943748905471…53547228775736606719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.267 Γ— 10⁹⁸(99-digit number)
12674387943748905471…53547228775736606721
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
2.534 Γ— 10⁹⁸(99-digit number)
25348775887497810942…07094457551473213439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.534 Γ— 10⁹⁸(99-digit number)
25348775887497810942…07094457551473213441
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
5.069 Γ— 10⁹⁸(99-digit number)
50697551774995621885…14188915102946426879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.069 Γ— 10⁹⁸(99-digit number)
50697551774995621885…14188915102946426881
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
1.013 Γ— 10⁹⁹(100-digit number)
10139510354999124377…28377830205892853759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.013 Γ— 10⁹⁹(100-digit number)
10139510354999124377…28377830205892853761
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
2.027 Γ— 10⁹⁹(100-digit number)
20279020709998248754…56755660411785707519
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:57,912,236 XPMΒ·at block #6,833,504 Β· updates every 60s
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