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Block #1,493,690

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/12/2016, 11:04:48 AM Β· Difficulty 10.6655 Β· 5,343,179 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c7ddd1eafe04c499294a5b0bda3d697cc0169455fe48ee108c5aeae7aaeeeec6
View on Chainz β†—

Height

#1,493,690

Difficulty

10.665476

Transactions

1

Size

200 B

Version

2

Bits

0aaa5ca0

Nonce

401,663,636

Timestamp

3/12/2016, 11:04:48 AM

Confirmations

5,343,179

Mined by

⛏️ P2SHANhQpHdMBrLFx5EYvnG2beNaitT16MR6gU

Merkle Root

fea3fae7932bb99af88f0eda02185806fe1c8ba46e4f2a034b3b3f60fcab14c1
Transactions (1)
Coinbasefea3fae7932bb9…3b3f60fcab14c1
1 in β†’ 1 out8.7800 XPM110 B
ANhQpHdM…T16MR6gU
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.

7.775 Γ— 10⁹⁡(96-digit number)
77752849680531346021…63578401006932131839
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
7.775 Γ— 10⁹⁡(96-digit number)
77752849680531346021…63578401006932131839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.775 Γ— 10⁹⁡(96-digit number)
77752849680531346021…63578401006932131841
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
1.555 Γ— 10⁹⁢(97-digit number)
15550569936106269204…27156802013864263679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.555 Γ— 10⁹⁢(97-digit number)
15550569936106269204…27156802013864263681
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
3.110 Γ— 10⁹⁢(97-digit number)
31101139872212538408…54313604027728527359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.110 Γ— 10⁹⁢(97-digit number)
31101139872212538408…54313604027728527361
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
6.220 Γ— 10⁹⁢(97-digit number)
62202279744425076816…08627208055457054719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.220 Γ— 10⁹⁢(97-digit number)
62202279744425076816…08627208055457054721
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
1.244 Γ— 10⁹⁷(98-digit number)
12440455948885015363…17254416110914109439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.244 Γ— 10⁹⁷(98-digit number)
12440455948885015363…17254416110914109441
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:57,939,242 XPMΒ·at block #6,836,868 Β· updates every 60s
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