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Block #210,443

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/15/2013, 3:42:43 AM Β· Difficulty 9.9131 Β· 6,597,985 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e19b978237302a023fbe3e18cc70c5f097070723f0929cff0572ebf0e08cfee5
View on Chainz β†—

Height

#210,443

Difficulty

9.913069

Transactions

2

Size

2.15 KB

Version

2

Bits

09e9beea

Nonce

120,720

Timestamp

10/15/2013, 3:42:43 AM

Confirmations

6,597,985

Mined by

⛏️ P2SHAab2HB2z57Nnnmg2yTJeqwdmWCoocYKQJE

Merkle Root

5e6083d8e6e71680e3737673a2c9cb8b4a4556cfd401ca5c0bff4d9269b02ba7
Transactions (2)
Coinbase8fcf3c1c2fc589…72129469a04862
1 in β†’ 1 out10.1900 XPM109 B
Aab2HB2z…oocYKQJE
1ab3be709fef05…bbd2858ba5bb37
13 in β†’ 2 out147.5202 XPM1.95 KB
ALpthvGg…D1g5z4CTAJ7ZwWg1…GxsrujWM
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.

1.614 Γ— 10⁹⁴(95-digit number)
16148285808536531074…47269326191611187759
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
1.614 Γ— 10⁹⁴(95-digit number)
16148285808536531074…47269326191611187759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.614 Γ— 10⁹⁴(95-digit number)
16148285808536531074…47269326191611187761
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
3.229 Γ— 10⁹⁴(95-digit number)
32296571617073062148…94538652383222375519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.229 Γ— 10⁹⁴(95-digit number)
32296571617073062148…94538652383222375521
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
6.459 Γ— 10⁹⁴(95-digit number)
64593143234146124296…89077304766444751039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.459 Γ— 10⁹⁴(95-digit number)
64593143234146124296…89077304766444751041
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
1.291 Γ— 10⁹⁡(96-digit number)
12918628646829224859…78154609532889502079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.291 Γ— 10⁹⁡(96-digit number)
12918628646829224859…78154609532889502081
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
2.583 Γ— 10⁹⁡(96-digit number)
25837257293658449718…56309219065779004159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.583 Γ— 10⁹⁡(96-digit number)
25837257293658449718…56309219065779004161
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:57,711,484 XPMΒ·at block #6,808,427 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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