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Block #2,833,178

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2018, 2:00:05 PM Β· Difficulty 11.7148 Β· 4,009,567 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
04d4d575916e4d8bab6bf8c9d0e80f6d1278a2b23dddf9f92684b589748f5e9e
View on Chainz β†—

Height

#2,833,178

Difficulty

11.714786

Transactions

1

Size

200 B

Version

2

Bits

0bb6fc37

Nonce

925,388,509

Timestamp

9/10/2018, 2:00:05 PM

Confirmations

4,009,567

Mined by

⛏️ P2SHANAM7SaFjhMJU4njt9J1TsjJzXn4uxyZdQ

Merkle Root

08b74f0b507cbaa330c7c6d2eceb435d14596eaf33271434b26a01e10e98cdd2
Transactions (1)
Coinbase08b74f0b507cba…6a01e10e98cdd2
1 in β†’ 1 out7.2700 XPM110 B
ANAM7SaF…n4uxyZdQ
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.

8.527 Γ— 10⁹³(94-digit number)
85270068603141793344…63946120515126732799
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
8.527 Γ— 10⁹³(94-digit number)
85270068603141793344…63946120515126732799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.527 Γ— 10⁹³(94-digit number)
85270068603141793344…63946120515126732801
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
1.705 Γ— 10⁹⁴(95-digit number)
17054013720628358668…27892241030253465599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.705 Γ— 10⁹⁴(95-digit number)
17054013720628358668…27892241030253465601
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
3.410 Γ— 10⁹⁴(95-digit number)
34108027441256717337…55784482060506931199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.410 Γ— 10⁹⁴(95-digit number)
34108027441256717337…55784482060506931201
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
6.821 Γ— 10⁹⁴(95-digit number)
68216054882513434675…11568964121013862399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.821 Γ— 10⁹⁴(95-digit number)
68216054882513434675…11568964121013862401
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
1.364 Γ— 10⁹⁡(96-digit number)
13643210976502686935…23137928242027724799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.364 Γ— 10⁹⁡(96-digit number)
13643210976502686935…23137928242027724801
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
2.728 Γ— 10⁹⁡(96-digit number)
27286421953005373870…46275856484055449599
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:57,986,296 XPMΒ·at block #6,842,744 Β· updates every 60s
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