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Block #99,248

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2013, 2:39:08 PM Β· Difficulty 9.3796 Β· 6,697,453 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8525a793eb6d3ecbcd6f033bf57f0d0720a0d6066ba9289e0993161ae4cf717
View on Chainz β†—

Height

#99,248

Difficulty

9.379586

Transactions

1

Size

200 B

Version

2

Bits

09612c8f

Nonce

291,111

Timestamp

8/5/2013, 2:39:08 PM

Confirmations

6,697,453

Mined by

⛏️ P2SHALJ24E54cDPzoVYd8isCythp1DCM192Nmg

Merkle Root

987595512946bfaa9901f21e6df387de336799c6cded81305caef33b30e77e52
Transactions (1)
Coinbase987595512946bf…aef33b30e77e52
1 in β†’ 1 out11.3500 XPM109 B
ALJ24E54…CM192Nmg
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.

1.116 Γ— 10⁹⁸(99-digit number)
11166757701001225108…97752310066322299539
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
1.116 Γ— 10⁹⁸(99-digit number)
11166757701001225108…97752310066322299539
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.116 Γ— 10⁹⁸(99-digit number)
11166757701001225108…97752310066322299541
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
2.233 Γ— 10⁹⁸(99-digit number)
22333515402002450217…95504620132644599079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.233 Γ— 10⁹⁸(99-digit number)
22333515402002450217…95504620132644599081
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
4.466 Γ— 10⁹⁸(99-digit number)
44667030804004900434…91009240265289198159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.466 Γ— 10⁹⁸(99-digit number)
44667030804004900434…91009240265289198161
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
8.933 Γ— 10⁹⁸(99-digit number)
89334061608009800869…82018480530578396319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.933 Γ— 10⁹⁸(99-digit number)
89334061608009800869…82018480530578396321
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
1.786 Γ— 10⁹⁹(100-digit number)
17866812321601960173…64036961061156792639
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:57,617,609 XPMΒ·at block #6,796,700 Β· updates every 60s
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