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Block #2,647,755

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/4/2018, 2:40:58 AM Β· Difficulty 11.7622 Β· 4,184,073 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bb01a92f90a26556e7d2580de9859c3f3d28c3ec0e2196a125dcbb95d778b8bd
View on Chainz β†—

Height

#2,647,755

Difficulty

11.762191

Transactions

2

Size

722 B

Version

2

Bits

0bc31ef2

Nonce

890,065,608

Timestamp

5/4/2018, 2:40:58 AM

Confirmations

4,184,073

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

30722c853be79e42789c17776b692a4c43d3ab275346a902d08d082b35c3af87
Transactions (2)
Coinbaseb70f5cd0061746…0b87c4069464e7
1 in β†’ 1 out7.2300 XPM110 B
Adqah8zh…1WwoHJ9t
3e0c060272ff4c…adf000ddde44d5
3 in β†’ 2 out1900.0103 XPM522 B
Ae68ZJak…bryAmvHjAcwQfQHY…C2hkXuZ1
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.

2.472 Γ— 10⁹⁴(95-digit number)
24723704172831282954…02878340003023667199
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
2.472 Γ— 10⁹⁴(95-digit number)
24723704172831282954…02878340003023667199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.472 Γ— 10⁹⁴(95-digit number)
24723704172831282954…02878340003023667201
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
4.944 Γ— 10⁹⁴(95-digit number)
49447408345662565909…05756680006047334399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.944 Γ— 10⁹⁴(95-digit number)
49447408345662565909…05756680006047334401
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
9.889 Γ— 10⁹⁴(95-digit number)
98894816691325131819…11513360012094668799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.889 Γ— 10⁹⁴(95-digit number)
98894816691325131819…11513360012094668801
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
1.977 Γ— 10⁹⁡(96-digit number)
19778963338265026363…23026720024189337599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.977 Γ— 10⁹⁡(96-digit number)
19778963338265026363…23026720024189337601
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
3.955 Γ— 10⁹⁡(96-digit number)
39557926676530052727…46053440048378675199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.955 Γ— 10⁹⁡(96-digit number)
39557926676530052727…46053440048378675201
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
7.911 Γ— 10⁹⁡(96-digit number)
79115853353060105455…92106880096757350399
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:57,898,742 XPMΒ·at block #6,831,827 Β· updates every 60s
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