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Block #1,345,090

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/28/2015, 12:59:03 AM Β· Difficulty 10.8183 Β· 5,472,619 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bf3d9edbc099fa790fec3aa8e4c3ce2223d5e5b97181346a3da8a7a92350f0e0
View on Chainz β†—

Height

#1,345,090

Difficulty

10.818271

Transactions

3

Size

4.36 KB

Version

2

Bits

0ad17a3b

Nonce

795,746,580

Timestamp

11/28/2015, 12:59:03 AM

Confirmations

5,472,619

Mined by

⛏️ P2SHASnKC3PgZTmenZuMkwSCVY1KDf677ybhUZ

Merkle Root

7faa0bec461df60edcd24746e4fdb007f5b60be6806a4451e1f96b7f8d8495a2
Transactions (3)
Coinbase1ed20fc86ab016…f138d37301e23c
1 in β†’ 1 out8.5900 XPM110 B
ASnKC3Pg…677ybhUZ
7211ed545c80ea…f980620035726a
9 in β†’ 2 out25.3162 XPM1.38 KB
AetR59tC…2Hy4r6r1AbecWDS9…1vtToSML
8dfe143e1cf2e4…16e8e1d767754a
19 in β†’ 1 out6.4093 XPM2.79 KB
AbecWDS9…1vtToSML
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.

8.202 Γ— 10⁹⁡(96-digit number)
82020712064330460521…96033093108559230719
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
8.202 Γ— 10⁹⁡(96-digit number)
82020712064330460521…96033093108559230719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.202 Γ— 10⁹⁡(96-digit number)
82020712064330460521…96033093108559230721
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
1.640 Γ— 10⁹⁢(97-digit number)
16404142412866092104…92066186217118461439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.640 Γ— 10⁹⁢(97-digit number)
16404142412866092104…92066186217118461441
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
3.280 Γ— 10⁹⁢(97-digit number)
32808284825732184208…84132372434236922879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.280 Γ— 10⁹⁢(97-digit number)
32808284825732184208…84132372434236922881
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
6.561 Γ— 10⁹⁢(97-digit number)
65616569651464368417…68264744868473845759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.561 Γ— 10⁹⁢(97-digit number)
65616569651464368417…68264744868473845761
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
1.312 Γ— 10⁹⁷(98-digit number)
13123313930292873683…36529489736947691519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.312 Γ— 10⁹⁷(98-digit number)
13123313930292873683…36529489736947691521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,785,731 XPMΒ·at block #6,817,708 Β· updates every 60s
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