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Block #1,113,481

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/17/2015, 4:43:57 PM Β· Difficulty 10.9052 Β· 5,727,653 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d3e2515e0bba2ddf9eef9f8e89dfc33b76772b27e8bd24b676e5f940b5c5ca6e
View on Chainz β†—

Height

#1,113,481

Difficulty

10.905240

Transactions

1

Size

201 B

Version

2

Bits

0ae7bdd7

Nonce

1,066,623,853

Timestamp

6/17/2015, 4:43:57 PM

Confirmations

5,727,653

Mined by

⛏️ P2SHAUULQ3cePXvKqHVSPL21NgXNC3Z9BBVStm

Merkle Root

8495cf7a273aca0323f93709c3ab5b725741b8a0fd3879ffe7fc4f8f7f8d882b
Transactions (1)
Coinbase8495cf7a273aca…fc4f8f7f8d882b
1 in β†’ 1 out8.4000 XPM110 B
AUULQ3ce…Z9BBVStm
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.

4.347 Γ— 10⁹⁷(98-digit number)
43470021489121942775…13683723739717959679
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
4.347 Γ— 10⁹⁷(98-digit number)
43470021489121942775…13683723739717959679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.347 Γ— 10⁹⁷(98-digit number)
43470021489121942775…13683723739717959681
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
8.694 Γ— 10⁹⁷(98-digit number)
86940042978243885551…27367447479435919359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.694 Γ— 10⁹⁷(98-digit number)
86940042978243885551…27367447479435919361
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
1.738 Γ— 10⁹⁸(99-digit number)
17388008595648777110…54734894958871838719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.738 Γ— 10⁹⁸(99-digit number)
17388008595648777110…54734894958871838721
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
3.477 Γ— 10⁹⁸(99-digit number)
34776017191297554220…09469789917743677439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.477 Γ— 10⁹⁸(99-digit number)
34776017191297554220…09469789917743677441
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
6.955 Γ— 10⁹⁸(99-digit number)
69552034382595108440…18939579835487354879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.955 Γ— 10⁹⁸(99-digit number)
69552034382595108440…18939579835487354881
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:57,973,442 XPMΒ·at block #6,841,133 Β· updates every 60s
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