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Block #2,610,335

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/12/2018, 6:43:43 AM Β· Difficulty 11.2193 Β· 4,216,627 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b04c8e9ce102e5ebe56d766e7ba54b6e4ae3ac5cd0b2f2947f06dcac365a133c
View on Chainz β†—

Height

#2,610,335

Difficulty

11.219256

Transactions

2

Size

869 B

Version

2

Bits

0b38212f

Nonce

1,286,614,933

Timestamp

4/12/2018, 6:43:43 AM

Confirmations

4,216,627

Mined by

⛏️ P2SHALaQv2i5pK1oyMjDWozgKxqMhYTY4L3k5C

Merkle Root

c097768aabd38b09a5a373cc1a2caf67aa22cc79cb35fe8e48f32fb2164e0382
Transactions (2)
Coinbased37d7156953588…6428020cfec0d0
1 in β†’ 1 out7.9400 XPM109 B
ALaQv2i5…TY4L3k5C
80b9d100804d8b…147bdf78b3faf8
4 in β†’ 2 out2700.0099 XPM671 B
AZA5wove…38TxSikLAaftQQdL…VsnTsiXY
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.

1.519 Γ— 10⁹³(94-digit number)
15194926773001602188…89171074581954847999
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
1.519 Γ— 10⁹³(94-digit number)
15194926773001602188…89171074581954847999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.519 Γ— 10⁹³(94-digit number)
15194926773001602188…89171074581954848001
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
3.038 Γ— 10⁹³(94-digit number)
30389853546003204376…78342149163909695999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.038 Γ— 10⁹³(94-digit number)
30389853546003204376…78342149163909696001
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
6.077 Γ— 10⁹³(94-digit number)
60779707092006408752…56684298327819391999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.077 Γ— 10⁹³(94-digit number)
60779707092006408752…56684298327819392001
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
1.215 Γ— 10⁹⁴(95-digit number)
12155941418401281750…13368596655638783999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.215 Γ— 10⁹⁴(95-digit number)
12155941418401281750…13368596655638784001
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
2.431 Γ— 10⁹⁴(95-digit number)
24311882836802563501…26737193311277567999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.431 Γ— 10⁹⁴(95-digit number)
24311882836802563501…26737193311277568001
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
4.862 Γ— 10⁹⁴(95-digit number)
48623765673605127002…53474386622555135999
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:57,859,872 XPMΒ·at block #6,826,961 Β· updates every 60s
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