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Block #2,090,624

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/27/2017, 9:40:15 PM Β· Difficulty 10.8742 Β· 4,742,589 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b724f727ae686d9af9c4e422806740f54b491c35335c9ea43cfaf72facbf8db8
View on Chainz β†—

Height

#2,090,624

Difficulty

10.874234

Transactions

1

Size

200 B

Version

2

Bits

0adfcdc7

Nonce

249,052,260

Timestamp

4/27/2017, 9:40:15 PM

Confirmations

4,742,589

Mined by

⛏️ P2SHAJiVCnAhuBCtWYwgsHtxM4Lh6HniYwZDJp

Merkle Root

6cc15e21b585f2dcd253e18e6957cceaaef6ade65aea9514c06de5ad023aae70
Transactions (1)
Coinbase6cc15e21b585f2…6de5ad023aae70
1 in β†’ 1 out8.4400 XPM110 B
AJiVCnAh…niYwZDJp
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.

5.802 Γ— 10⁹³(94-digit number)
58025196133858885723…78295157843942772159
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
5.802 Γ— 10⁹³(94-digit number)
58025196133858885723…78295157843942772159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.802 Γ— 10⁹³(94-digit number)
58025196133858885723…78295157843942772161
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
1.160 Γ— 10⁹⁴(95-digit number)
11605039226771777144…56590315687885544319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.160 Γ— 10⁹⁴(95-digit number)
11605039226771777144…56590315687885544321
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
2.321 Γ— 10⁹⁴(95-digit number)
23210078453543554289…13180631375771088639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.321 Γ— 10⁹⁴(95-digit number)
23210078453543554289…13180631375771088641
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
4.642 Γ— 10⁹⁴(95-digit number)
46420156907087108578…26361262751542177279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.642 Γ— 10⁹⁴(95-digit number)
46420156907087108578…26361262751542177281
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
9.284 Γ— 10⁹⁴(95-digit number)
92840313814174217156…52722525503084354559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.284 Γ— 10⁹⁴(95-digit number)
92840313814174217156…52722525503084354561
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:57,909,890 XPMΒ·at block #6,833,212 Β· updates every 60s
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