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Block #103,497

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2013, 3:12:32 PM Β· Difficulty 9.5272 Β· 6,723,261 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0ebab27ef17e8e0aceeda5fffc7ea652113002b0af0604612b89b6c9cdc3a249
View on Chainz β†—

Height

#103,497

Difficulty

9.527153

Transactions

1

Size

199 B

Version

2

Bits

0986f37b

Nonce

390,794

Timestamp

8/7/2013, 3:12:32 PM

Confirmations

6,723,261

Mined by

⛏️ P2SHAYSqifmRAoU9fkR5nEwa1iudtwYUncQMmR

Merkle Root

da44108a495cecf9331d996a9a8b5e905d053f8bfdd6b4d5312c157535e1fd94
Transactions (1)
Coinbaseda44108a495cec…2c157535e1fd94
1 in β†’ 1 out11.0000 XPM109 B
AYSqifmR…YUncQMmR
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.

9.148 Γ— 10⁹⁴(95-digit number)
91488190158928233434…22483222060164023339
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
9.148 Γ— 10⁹⁴(95-digit number)
91488190158928233434…22483222060164023339
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.148 Γ— 10⁹⁴(95-digit number)
91488190158928233434…22483222060164023341
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
1.829 Γ— 10⁹⁡(96-digit number)
18297638031785646686…44966444120328046679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.829 Γ— 10⁹⁡(96-digit number)
18297638031785646686…44966444120328046681
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
3.659 Γ— 10⁹⁡(96-digit number)
36595276063571293373…89932888240656093359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.659 Γ— 10⁹⁡(96-digit number)
36595276063571293373…89932888240656093361
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
7.319 Γ— 10⁹⁡(96-digit number)
73190552127142586747…79865776481312186719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.319 Γ— 10⁹⁡(96-digit number)
73190552127142586747…79865776481312186721
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
1.463 Γ— 10⁹⁢(97-digit number)
14638110425428517349…59731552962624373439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.463 Γ— 10⁹⁢(97-digit number)
14638110425428517349…59731552962624373441
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:57,858,223 XPMΒ·at block #6,826,757 Β· updates every 60s
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