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Block #2,094,631

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/30/2017, 5:48:40 PM Β· Difficulty 10.8723 Β· 4,745,042 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b62d6df1cc64c6db707cecad84ab2e726b559d79b2139d45cb72e95360df117d
View on Chainz β†—

Height

#2,094,631

Difficulty

10.872301

Transactions

2

Size

1.43 KB

Version

2

Bits

0adf4f21

Nonce

73,371,444

Timestamp

4/30/2017, 5:48:40 PM

Confirmations

4,745,042

Mined by

⛏️ P2SHAU4GVFmubmf7BZ6tk5dyUBViv9WZ84SKoF

Merkle Root

f5814543b343a4f34cd62770f68a867524321cd60b5c06f9a787ea126d5c2305
Transactions (2)
Coinbase979a3c3aa6a793…95292997f8b5fd
1 in β†’ 1 out8.4700 XPM109 B
AU4GVFmu…WZ84SKoF
6e2b43f254ab4b…256f0f6cc4ab39
8 in β†’ 2 out4080.9428 XPM1.23 KB
ATXq5KR7…hXkX5wZFAWFYixUG…4nL4F5Bp
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.

3.475 Γ— 10⁹⁷(98-digit number)
34757568542286069325…22210703888213360639
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
3.475 Γ— 10⁹⁷(98-digit number)
34757568542286069325…22210703888213360639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.475 Γ— 10⁹⁷(98-digit number)
34757568542286069325…22210703888213360641
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
6.951 Γ— 10⁹⁷(98-digit number)
69515137084572138650…44421407776426721279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.951 Γ— 10⁹⁷(98-digit number)
69515137084572138650…44421407776426721281
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
1.390 Γ— 10⁹⁸(99-digit number)
13903027416914427730…88842815552853442559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.390 Γ— 10⁹⁸(99-digit number)
13903027416914427730…88842815552853442561
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
2.780 Γ— 10⁹⁸(99-digit number)
27806054833828855460…77685631105706885119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.780 Γ— 10⁹⁸(99-digit number)
27806054833828855460…77685631105706885121
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
5.561 Γ— 10⁹⁸(99-digit number)
55612109667657710920…55371262211413770239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.561 Γ— 10⁹⁸(99-digit number)
55612109667657710920…55371262211413770241
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:57,961,673 XPMΒ·at block #6,839,672 Β· updates every 60s
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