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Block #1,113,482

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/17/2015, 4:44:48 PM Β· Difficulty 10.9052 Β· 5,729,819 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
849890a51d092c99b6ed7ca0feb674cece50f77fe2f36e23d879229a37f150c8
View on Chainz β†—

Height

#1,113,482

Difficulty

10.905238

Transactions

1

Size

201 B

Version

2

Bits

0ae7bdad

Nonce

2,048,497,186

Timestamp

6/17/2015, 4:44:48 PM

Confirmations

5,729,819

Mined by

⛏️ P2SHAWEpnAP7RQFCLDqDUHfk67Ysg748jFXVoe

Merkle Root

159f31b3da293779a880b7838ee6533d46ce4ea49c0bac5959463b7346fe3cf3
Transactions (1)
Coinbase159f31b3da2937…463b7346fe3cf3
1 in β†’ 1 out8.4000 XPM110 B
AWEpnAP7…48jFXVoe
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.

1.781 Γ— 10⁹⁷(98-digit number)
17814569994206889100…64200080971166392319
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
1.781 Γ— 10⁹⁷(98-digit number)
17814569994206889100…64200080971166392319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.781 Γ— 10⁹⁷(98-digit number)
17814569994206889100…64200080971166392321
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
3.562 Γ— 10⁹⁷(98-digit number)
35629139988413778201…28400161942332784639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.562 Γ— 10⁹⁷(98-digit number)
35629139988413778201…28400161942332784641
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
7.125 Γ— 10⁹⁷(98-digit number)
71258279976827556402…56800323884665569279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.125 Γ— 10⁹⁷(98-digit number)
71258279976827556402…56800323884665569281
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
1.425 Γ— 10⁹⁸(99-digit number)
14251655995365511280…13600647769331138559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.425 Γ— 10⁹⁸(99-digit number)
14251655995365511280…13600647769331138561
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
2.850 Γ— 10⁹⁸(99-digit number)
28503311990731022560…27201295538662277119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.850 Γ— 10⁹⁸(99-digit number)
28503311990731022560…27201295538662277121
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:57,990,773 XPMΒ·at block #6,843,300 Β· updates every 60s
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