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Block #2,140,943

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/1/2017, 9:39:31 PM Β· Difficulty 10.8742 Β· 4,700,741 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6f4f6c09132478eb8a16468fe2821966a91253983e77dfcbc4a7f7a033dac45c
View on Chainz β†—

Height

#2,140,943

Difficulty

10.874175

Transactions

2

Size

722 B

Version

2

Bits

0adfc9ed

Nonce

448,144,307

Timestamp

6/1/2017, 9:39:31 PM

Confirmations

4,700,741

Mined by

⛏️ P2SHAKRfH7HNVyj7KDFJmSQ3fFmDsGWxF8ayXn

Merkle Root

08d2cab143f32abca232a6de3de48d87f06a2a167782bfd089d65b1a21da66aa
Transactions (2)
Coinbase341b50e776e828…9ba32fd556def6
1 in β†’ 1 out8.4500 XPM110 B
AKRfH7HN…WxF8ayXn
a20987354891a2…1c358712c38b39
3 in β†’ 2 out99.0227 XPM522 B
AZgLo1oV…ekVipSafAWQtBsY5…FEjq8QMC
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.

1.444 Γ— 10⁹⁡(96-digit number)
14446665771304965192…98273460892198499199
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
1.444 Γ— 10⁹⁡(96-digit number)
14446665771304965192…98273460892198499199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.444 Γ— 10⁹⁡(96-digit number)
14446665771304965192…98273460892198499201
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
2.889 Γ— 10⁹⁡(96-digit number)
28893331542609930385…96546921784396998399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.889 Γ— 10⁹⁡(96-digit number)
28893331542609930385…96546921784396998401
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
5.778 Γ— 10⁹⁡(96-digit number)
57786663085219860771…93093843568793996799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.778 Γ— 10⁹⁡(96-digit number)
57786663085219860771…93093843568793996801
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
1.155 Γ— 10⁹⁢(97-digit number)
11557332617043972154…86187687137587993599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.155 Γ— 10⁹⁢(97-digit number)
11557332617043972154…86187687137587993601
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
2.311 Γ— 10⁹⁢(97-digit number)
23114665234087944308…72375374275175987199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.311 Γ— 10⁹⁢(97-digit number)
23114665234087944308…72375374275175987201
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:57,977,861 XPMΒ·at block #6,841,683 Β· updates every 60s
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