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Block #2,684,871

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/30/2018, 7:35:04 PM Β· Difficulty 11.6912 Β· 4,152,049 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4bbb38ebee936db5bcb0849caa78b1f081e9929b2e010ee74b240212c1c0ce9e
View on Chainz β†—

Height

#2,684,871

Difficulty

11.691230

Transactions

2

Size

1.87 KB

Version

2

Bits

0bb0f474

Nonce

1,209,941,288

Timestamp

5/30/2018, 7:35:04 PM

Confirmations

4,152,049

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

8906976c825c9959aa4880bf93f5e6a4ec5492bb069a64e987d30ceb475387a0
Transactions (2)
Coinbaseab73826d150a51…642ede7efbcd2f
1 in β†’ 1 out7.3200 XPM110 B
Adqah8zh…1WwoHJ9t
027fac4261a5b8…7fca0666a72ea3
11 in β†’ 2 out4000.0099 XPM1.67 KB
AH3A2GJU…NLYdkucbAS7in59i…91URSwbU
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.

2.099 Γ— 10⁹⁸(99-digit number)
20993087285962909257…90576167700824145919
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
2.099 Γ— 10⁹⁸(99-digit number)
20993087285962909257…90576167700824145919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.099 Γ— 10⁹⁸(99-digit number)
20993087285962909257…90576167700824145921
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
4.198 Γ— 10⁹⁸(99-digit number)
41986174571925818514…81152335401648291839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.198 Γ— 10⁹⁸(99-digit number)
41986174571925818514…81152335401648291841
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
8.397 Γ— 10⁹⁸(99-digit number)
83972349143851637029…62304670803296583679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.397 Γ— 10⁹⁸(99-digit number)
83972349143851637029…62304670803296583681
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
1.679 Γ— 10⁹⁹(100-digit number)
16794469828770327405…24609341606593167359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.679 Γ— 10⁹⁹(100-digit number)
16794469828770327405…24609341606593167361
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
3.358 Γ— 10⁹⁹(100-digit number)
33588939657540654811…49218683213186334719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.358 Γ— 10⁹⁹(100-digit number)
33588939657540654811…49218683213186334721
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
6.717 Γ— 10⁹⁹(100-digit number)
67177879315081309623…98437366426372669439
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:57,939,655 XPMΒ·at block #6,836,919 Β· updates every 60s
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