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Block #2,650,961

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/6/2018, 11:38:39 AM Β· Difficulty 11.7521 Β· 4,185,557 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d155325ff83a71b9fb478fb58b7eba6ace176eea207b266e4e4b775c9ffe8b82
View on Chainz β†—

Height

#2,650,961

Difficulty

11.752078

Transactions

3

Size

1.00 KB

Version

2

Bits

0bc0882f

Nonce

490,607,516

Timestamp

5/6/2018, 11:38:39 AM

Confirmations

4,185,557

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

3cfd20ae8d39b9443b0582f58cd341da52091ddbd6c95342a714df6aed0021d1
Transactions (3)
Coinbase4285697568472d…4ae25bd325dc18
1 in β†’ 1 out7.2500 XPM109 B
Adqah8zh…1WwoHJ9t
6b5b807e524e58…054759e237e526
2 in β†’ 2 out11.6400 XPM340 B
AYH7AB2W…a9b548SuAVRj1vRq…R1MQnhjf
8ed2f8f226c79d…f105fa40962af5
3 in β†’ 2 out10.5000 XPM487 B
AJvyAX4p…vpSys3HNAVWg14NR…oJL8qpQX
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.

4.213 Γ— 10⁹⁡(96-digit number)
42134575926002719010…00385192375120688639
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
4.213 Γ— 10⁹⁡(96-digit number)
42134575926002719010…00385192375120688639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.213 Γ— 10⁹⁡(96-digit number)
42134575926002719010…00385192375120688641
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
8.426 Γ— 10⁹⁡(96-digit number)
84269151852005438021…00770384750241377279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.426 Γ— 10⁹⁡(96-digit number)
84269151852005438021…00770384750241377281
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
1.685 Γ— 10⁹⁢(97-digit number)
16853830370401087604…01540769500482754559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.685 Γ— 10⁹⁢(97-digit number)
16853830370401087604…01540769500482754561
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
3.370 Γ— 10⁹⁢(97-digit number)
33707660740802175208…03081539000965509119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.370 Γ— 10⁹⁢(97-digit number)
33707660740802175208…03081539000965509121
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
6.741 Γ— 10⁹⁢(97-digit number)
67415321481604350417…06163078001931018239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.741 Γ— 10⁹⁢(97-digit number)
67415321481604350417…06163078001931018241
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
1.348 Γ— 10⁹⁷(98-digit number)
13483064296320870083…12326156003862036479
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:57,936,421 XPMΒ·at block #6,836,517 Β· updates every 60s
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