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Block #2,097,443

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/2/2017, 5:12:09 PM Β· Difficulty 10.8716 Β· 4,728,216 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3cc4bc0978a63c0719427b9d86acb0ef73ec1ca180267de6286f9b182efa87dd
View on Chainz β†—

Height

#2,097,443

Difficulty

10.871585

Transactions

2

Size

80.91 KB

Version

2

Bits

0adf2038

Nonce

102,230,673

Timestamp

5/2/2017, 5:12:09 PM

Confirmations

4,728,216

Mined by

⛏️ P2SHAH9qMiLkX5uwFyXZDupzNgHWHQBTWALKkr

Merkle Root

b24e98e368541a9f0e6dfc43b0dead347e06c6d6a1afad6724c40f3686345bd4
Transactions (2)
Coinbase6fc1f2848267c9…b9cab8cc094d86
1 in β†’ 1 out9.2800 XPM109 B
AH9qMiLk…BTWALKkr
b87f835841145c…b5952da37c9e1b
558 in β†’ 2 out18.0100 XPM80.71 KB
Abtfz4Rn…4uSEQqzJAVaj27ki…Ntfy4Rjn
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.

1.905 Γ— 10⁹⁷(98-digit number)
19052507152933756599…08492660192031907839
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
1.905 Γ— 10⁹⁷(98-digit number)
19052507152933756599…08492660192031907839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.905 Γ— 10⁹⁷(98-digit number)
19052507152933756599…08492660192031907841
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
3.810 Γ— 10⁹⁷(98-digit number)
38105014305867513198…16985320384063815679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.810 Γ— 10⁹⁷(98-digit number)
38105014305867513198…16985320384063815681
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
7.621 Γ— 10⁹⁷(98-digit number)
76210028611735026396…33970640768127631359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.621 Γ— 10⁹⁷(98-digit number)
76210028611735026396…33970640768127631361
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
1.524 Γ— 10⁹⁸(99-digit number)
15242005722347005279…67941281536255262719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.524 Γ— 10⁹⁸(99-digit number)
15242005722347005279…67941281536255262721
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
3.048 Γ— 10⁹⁸(99-digit number)
30484011444694010558…35882563072510525439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.048 Γ— 10⁹⁸(99-digit number)
30484011444694010558…35882563072510525441
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:57,849,379 XPMΒ·at block #6,825,658 Β· updates every 60s
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