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Block #1,229,740

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/10/2015, 3:45:51 AM Β· Difficulty 10.7366 Β· 5,579,505 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
82447d9a9122b9dc43a476408a888fd03ba2ba12e2472b25b4d62123fb425f9f
View on Chainz β†—

Height

#1,229,740

Difficulty

10.736628

Transactions

2

Size

3.02 KB

Version

2

Bits

0abc93a0

Nonce

991,946,029

Timestamp

9/10/2015, 3:45:51 AM

Confirmations

5,579,505

Mined by

⛏️ P2SHAHh2hTkR3myLPau44GGmE4MLgWgMs4EfCj

Merkle Root

b0ed4ff1361f1837b90abc78efd09bde921e519a6eb1a2d9cc00c60a1019fd67
Transactions (2)
Coinbase7a80d2da4a0659…f2b558cd13a705
1 in β†’ 1 out8.6900 XPM110 B
AHh2hTkR…gMs4EfCj
a2a87883dd2ff9…848bb1bf549035
19 in β†’ 2 out18.1107 XPM2.82 KB
AJng1UsF…BqkQWD3bAb4tdH3y…jyjtGGxk
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.

1.021 Γ— 10⁹⁡(96-digit number)
10218103393836360771…98143936210227866879
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
1.021 Γ— 10⁹⁡(96-digit number)
10218103393836360771…98143936210227866879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.021 Γ— 10⁹⁡(96-digit number)
10218103393836360771…98143936210227866881
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
2.043 Γ— 10⁹⁡(96-digit number)
20436206787672721543…96287872420455733759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.043 Γ— 10⁹⁡(96-digit number)
20436206787672721543…96287872420455733761
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
4.087 Γ— 10⁹⁡(96-digit number)
40872413575345443086…92575744840911467519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.087 Γ— 10⁹⁡(96-digit number)
40872413575345443086…92575744840911467521
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
8.174 Γ— 10⁹⁡(96-digit number)
81744827150690886173…85151489681822935039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.174 Γ— 10⁹⁡(96-digit number)
81744827150690886173…85151489681822935041
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
1.634 Γ— 10⁹⁢(97-digit number)
16348965430138177234…70302979363645870079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.634 Γ— 10⁹⁢(97-digit number)
16348965430138177234…70302979363645870081
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:57,718,025 XPMΒ·at block #6,809,244 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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