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Block #103,541

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2013, 3:38:49 PM Β· Difficulty 9.5288 Β· 6,700,129 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c1207f0204a68d0123b1397002465781f6d0c7f635c02616b855cba6c4999903
View on Chainz β†—

Height

#103,541

Difficulty

9.528807

Transactions

1

Size

201 B

Version

2

Bits

09875fe7

Nonce

112,502

Timestamp

8/7/2013, 3:38:49 PM

Confirmations

6,700,129

Mined by

⛏️ P2SHAezMwyLP2hpT3yh3LDZkydqkpsrTg7Eyfk

Merkle Root

0d6d6c9becf2f4ba19f8c96b184f000389020cffddc69373934b697984bbec04
Transactions (1)
Coinbase0d6d6c9becf2f4…4b697984bbec04
1 in β†’ 1 out11.0000 XPM109 B
AezMwyLP…rTg7Eyfk
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.

3.286 Γ— 10⁹⁸(99-digit number)
32863760097200542370…33338614005500600959
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
3.286 Γ— 10⁹⁸(99-digit number)
32863760097200542370…33338614005500600959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.286 Γ— 10⁹⁸(99-digit number)
32863760097200542370…33338614005500600961
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
6.572 Γ— 10⁹⁸(99-digit number)
65727520194401084740…66677228011001201919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.572 Γ— 10⁹⁸(99-digit number)
65727520194401084740…66677228011001201921
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
1.314 Γ— 10⁹⁹(100-digit number)
13145504038880216948…33354456022002403839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.314 Γ— 10⁹⁹(100-digit number)
13145504038880216948…33354456022002403841
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
2.629 Γ— 10⁹⁹(100-digit number)
26291008077760433896…66708912044004807679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.629 Γ— 10⁹⁹(100-digit number)
26291008077760433896…66708912044004807681
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
5.258 Γ— 10⁹⁹(100-digit number)
52582016155520867792…33417824088009615359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,673,396 XPMΒ·at block #6,803,669 Β· updates every 60s
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