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Block #1,634,326

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/18/2016, 6:11:43 PM Β· Difficulty 10.6060 Β· 5,207,771 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d0b4525f58134c7d2c60b23ed305dc76dd87a865eacb165890b6b7214b33eb35
View on Chainz β†—

Height

#1,634,326

Difficulty

10.606027

Transactions

2

Size

2.73 KB

Version

2

Bits

0a9b2494

Nonce

281,064,390

Timestamp

6/18/2016, 6:11:43 PM

Confirmations

5,207,771

Mined by

⛏️ P2SHAYb2tt371Kw2RNxe9XLeLx2cLe2NvrKwPX

Merkle Root

cd5ff1e434ecbf51cbffb3e1654dc85df2c9975520b79f762ddf682791223eba
Transactions (2)
Coinbased49788dfa28e48…39ff4feef7c54a
1 in β†’ 1 out8.9300 XPM109 B
AYb2tt37…2NvrKwPX
8ab5694494e8b5…5809f82ada4701
17 in β†’ 2 out40.0100 XPM2.53 KB
AcPR5WgD…X1ReK5m1AYpTr9AK…vVczSFU6
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.

1.730 Γ— 10⁹⁢(97-digit number)
17300640533728006531…23330044570674181119
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
1.730 Γ— 10⁹⁢(97-digit number)
17300640533728006531…23330044570674181119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.730 Γ— 10⁹⁢(97-digit number)
17300640533728006531…23330044570674181121
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
3.460 Γ— 10⁹⁢(97-digit number)
34601281067456013062…46660089141348362239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.460 Γ— 10⁹⁢(97-digit number)
34601281067456013062…46660089141348362241
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
6.920 Γ— 10⁹⁢(97-digit number)
69202562134912026125…93320178282696724479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.920 Γ— 10⁹⁢(97-digit number)
69202562134912026125…93320178282696724481
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
1.384 Γ— 10⁹⁷(98-digit number)
13840512426982405225…86640356565393448959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.384 Γ— 10⁹⁷(98-digit number)
13840512426982405225…86640356565393448961
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
2.768 Γ— 10⁹⁷(98-digit number)
27681024853964810450…73280713130786897919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.768 Γ— 10⁹⁷(98-digit number)
27681024853964810450…73280713130786897921
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:57,981,162 XPMΒ·at block #6,842,096 Β· updates every 60s
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