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Block #2,148,798

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/6/2017, 4:53:44 PM Β· Difficulty 10.8958 Β· 4,696,328 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
65c8e318ec1140d997f2e10b28fee84e2079db4867922659e5e0f6a45ae627db
View on Chainz β†—

Height

#2,148,798

Difficulty

10.895804

Transactions

1

Size

200 B

Version

2

Bits

0ae5536b

Nonce

546,875,711

Timestamp

6/6/2017, 4:53:44 PM

Confirmations

4,696,328

Mined by

⛏️ P2SHANqgGpttqUqroPMTUw6N4K8CYysxjWZiRC

Merkle Root

aa9f2f217a5bb43f966aeef0d6b526b23880819196ccc965de89026973be09b4
Transactions (1)
Coinbaseaa9f2f217a5bb4…89026973be09b4
1 in β†’ 1 out8.4100 XPM109 B
ANqgGptt…sxjWZiRC
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.

7.633 Γ— 10⁹⁢(97-digit number)
76337343091796895212…09658587981108203519
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
7.633 Γ— 10⁹⁢(97-digit number)
76337343091796895212…09658587981108203519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.633 Γ— 10⁹⁢(97-digit number)
76337343091796895212…09658587981108203521
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
1.526 Γ— 10⁹⁷(98-digit number)
15267468618359379042…19317175962216407039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.526 Γ— 10⁹⁷(98-digit number)
15267468618359379042…19317175962216407041
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
3.053 Γ— 10⁹⁷(98-digit number)
30534937236718758084…38634351924432814079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.053 Γ— 10⁹⁷(98-digit number)
30534937236718758084…38634351924432814081
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
6.106 Γ— 10⁹⁷(98-digit number)
61069874473437516169…77268703848865628159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.106 Γ— 10⁹⁷(98-digit number)
61069874473437516169…77268703848865628161
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
1.221 Γ— 10⁹⁸(99-digit number)
12213974894687503233…54537407697731256319
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.221 Γ— 10⁹⁸(99-digit number)
12213974894687503233…54537407697731256321
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:58,005,435 XPMΒ·at block #6,845,125 Β· updates every 60s
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